Thank you, Arthur.

After messing around with it, I realized the colored wires that terminate in the plastic plug--the wires *from* the car that go into the circuit board--were indeed twisted round once or twice. This seemingly benign situation, I think, was the cause of the trouble. Because after untwisting the helix of wires and reconnecting, everything's fine :)

Thanks for the advice--I hope this post will help someone else some day--I was ready to try all sorts of other, more complicated/expensive approaches!

JM