Updated: 6 hours ago
Discussing the general subject of UFOs (recently rebranded UAP - Unidentified Aerial Phenomena - by the US military) has become almost respectable since the June 2021 publication of the Pentagon's UAP report. The report didn't reveal anything dramatic, just more or less stating; "These objects have been seen by military personnel and recorded by various sensor platforms doing manoeuvres impossible for our technology. There's no suggestion that they are from a foreign adversary [or of alien origin], but the matter requires further research."  There is an interesting and fairly well documented aspect of the phenomena. Over the decades hundreds of reports from across the world have accumulated of motor vehicle engines cutting out during a close encounter with a UFO.
The vehicle appears to act almost as an instrument - independent of the witness - in reacting to the event, sometimes reacting even before the witness saw anything unusual. The data seems to reveal a particular response suggesting the effect is genuine, as we shall see later. But to illustrate the phenomenon, here are some typical examples:
The first reported instance I could find was from 1909 - not of a car but a motorbike - when on 19 May at 1130 pm in Wroxham, Norfolk, a lone motorcyclist saw a globular light travelling in a straight trajectory overhead. During its passage, the motorcycle headlamp failed to operate. He stopped his machine when this occurred, but the headlamp began to operate once the object moved away and out of sight. 
Another was near RAF Fairford, Wiltshire, in 1969 (exact date unknown) where a family felt the air become electrified as the engine stalled and the car lights car went out. Their dog became quite agitated. They then saw three disc-shaped metallic objects moving in a V-formation high overhead. The car engine could be restarted after the discs had disappeared. 
Our next curios report is of an incident near Sopley, Hampshire, on 6 November 1967 where a cigar-shaped object - bright, phosphorescent green with a white bottom - approached a diesel lorry. The driver reported that the lights and radio went off but the engine continued running. He stopped his vehicle about 60 feet away from the object, which was moving now no more than 10 feet above the road. A Jaguar car approached the scene during the sighting and its electrics and engine failed. When the object moved slowly up into the sky both the truck and car then operated normally. 
In the final example a red luminous disc passed over two tractors in Forli, Italy, on 14 November 1954. One tractor had a diesel engine and the other a petrol engine. The diesel tractor continued to operate, but the other tractor’s engine stopped and could not be started until the UFO had vanished. 
These last two cases reveal a very interesting response which I hinted at above; the observation that diesel engines have rarely been reported to stall during a UFO encounter. Diesel engines don't have spark plugs, and nearly always continue to run during such an event, although their lights may dim or extinguish until the object moves away.
This petrol/diesel engine anomaly is the sort of observation that is unlikely to be erroneous or fictitious as it shows up in the data only when there are a sufficient number of reports. I think it lends credibility to there being a real phenomenon that is yet to be explained. It also implies that whatever UFOs are, they are associated with strong electrostatic or electromagnetic effects.
Most of the reports I have found are years, sometimes decades old. Unfortunately I have not found any contemporary reports relating to modern petrol and diesel vehicles having complex electronic engine-management systems. Such cases might give insight as to whether modern vehicles are more or less susceptible, and this data would very likely throw more light on the phenomenon.
There are two main theories as to what's happening regarding close-encounter engine stalling. One is that strongly ionised air reduces or prevents sparking at the plugs. The suggestion being that the glowing appearance around the object is a plasma, and this ionises the air around the object for some considerable distance. The ionised air prevents the the charge from building up sufficiently to allow a spark in the plug. Diesel engines (with mechanically controlled injectors) ignite the fuel by compression so they don't have an electrical input to keep running.
The other theory is that some form of very strong magnetic field interferes with the vehicle's electrical system, possibly by saturating the ignition-coil core and reducing its ability to generate high voltages for the spark plugs. BUFORA carried out an experiment in 1964 which, although not proving the case engine stalls were caused by strong magnetic fields, did provide some interesting supporting evidence. 
I'm minded to think this latter theory is the more plausible explanation, as it would also help explain some of the other noted effects on a vehicle's electrical systems and the occasionally reported localised interference with power distribution, radio and TV reception. But wouldn't a strong magnetic field leave significant residual magnetism in the vehicle's steel parts so be easily confirmed as an after-effect? Yes, if the magnetic field is not changing and is unidirectional like a that of the Earth, or a magnet. However, some observations suggest that the magnetic field is slowly oscillating, and as the object moves away the alternating field diminishes and demagnetises the vehicle, in exactly the same way that professional magnetic tape bulk erasers work. Nevertheless there have been cases where residual magnetism has been reported - including magnetising mechanical watches.
However, the magnetic field theory - whether it's an alternating field or not - is further supported by a case in Spain in February 1978 when a close encounter not only stopped the engine and magnetised the driver's watch, but it also apparently partially wiped a cassette tape. Unfortunately, given the number of cars that would have had music cassettes and cartridges, this is the only case I can find where the recording might have been demagnetised by the UFO. I expect the magnetic strip on bank and credit cards would also be affected - but again, I've not found any data for this. 
These electro-magnetic events are a special class of UFO encounter, which open the possibility for a UFO detection method. From the early 1960s UFO detectors of varying sophistication have been available to the public.
Serious UFO detection requires monitoring of many parameters. For example changes in background radiation; wide-band radio emission from ELF to beyond microwaves; radar interference; tiny changes in gravity and of course detecting the anomalous motion of aerial objects. This type of analysis is being carried out in the San Luis Valley, Colorado, where researcher Chris O'Brien is monitoring some of these parameters. 
This is a complex and expensive undertaking, but for decades followers of the UFO enigma have been encouraged to undertake their own monitoring using various magnetic anomaly detectors. Flying Saucer Review (FSR) published an all electronic detector circuit back in 1968. In the 1970s researcher Ray Stanford tried to establish a network of UFO detectors with his Project Starlight International, describing in his leaflet a couple of simple magnets-on-a-wire designs for people to make at home. As a teenager I remember saving up for the 'Skywatch UFO Detector' advertised in FSR for many years. Various electronics magazines have published construction details - often with a tongue-in-cheek attitude - and DIY plans of differing complexities are available from the internet. For the past few years even Amazon has been selling one. 
Some time ago I built one of my own detector/magnetometer using a Hall effect compass module. Like all the others mentioned, it is relatively crude and un-calibrated, but it has been triggered a number of times, although I doubt the cause was extra-terrestrial in origin!
All these designs are just basic magnetometers. There is already a network across the world of precision magnetometers for detecting changes in the Earth's magnetosphere caused by solar flares, coronal mass ejections, etc. But perhaps they are not sufficient in number nor designed to detect the relatively rapid changes the UFO phenomenon might create.
In the September 2015 edition of Fortean Times, Jenny Randles was prompted by 'Preston' - a mutual acquaintance - to write a piece about UFO detectors and how modern communications could create a network of devices. Although an interesting proposal, and an updated version of Ray Stanford's project that ended in the 1970s, nothing came of the suggestion. In conclusion, I have no idea what UFOs are, but I'm pretty sure a small percentage are a real, genuinely witnessed, unexplained phenomenon. To the surprise of many, the recent Pentagon report actually confirms this. The obscure reaction of different types of vehicle engine seems to indicate that these are not all just misidentified objects - they are real and create an observable specific pattern. Of course it remains to be seen what effect close encounters will have on electric cars.
So, if anyone wants to buy or build a magnetic UFO detector, please let us know...!
 https://www.dni.gov/files/ODNI/documents/assessments/Prelimary-Assessment-UAP-20210625.pdf  East Anglian Daily Times, May 21, 1909
 FSR Case Histories, Supplement no. 3
 Spacelink, Vol. 5, no. 1
 NICAP report, June 1960
 FSR, Vol 30, no. 3