To me (an electronics engineer) it sounds like your neighbor's alarm did not pass EMC immunity tests quite ok... and at the same time the car's tests were passe

To me (an electronics engineer) it sounds like your neighbor's alarm did not pass EMC immunity tests quite ok... and at the same time the car's tests were passed with way too thin margin. Or it could be that one of the alarm inputs is in high impedance, but then it should trigger to way more than just putting a car in reverse. Little bit of site surveying with portable spectrum analyzer may reveal something. Or playing around with wide-band emitters -- which may be illegal. Then again -- it may be something else. Good hint would be to know what sensor is triggered exactly. Usually alarm control panels tell that.