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Well, as long as the sections are galvanically connected to each other (most
likely) you will only need one connection spot.
Of course, if your car is e.g. a Corvette with a fibreglass body it won't work.
Be aware that you need a separate battery for the alarm, as the negative pole
of a car battery is connected to the chassis/body.
You could build a switched, isolated power supply for the circuit.
But I have my doubts that the circuit would work anyway as I am not clear on
its principle. Either it could be utilising the mains hum, which is picked up by our
bodies, but then it would only work in the presence of mains wiring.
Or it could use a charge transfer from the body to the touch plate - in which case
I believe the body of a car would be too big of a "plate", distributing the charge
over a large area. The example calls for a door knob as the touch plate,
which presumably gives a better effect.
That's a proximity alarm. I once saw an american car in a parking lot that
boomed out a voice saying "Move away from the car!" whenever someone
got close to it. Here is some information: https://www.clifford.com/uk/faq.asp#proximity
You can google on from there.