open car door - engine shuts off?

YUp ! I'll bet my quarter there IS an aftermarket bogger alarm under the dash somewhere.
A story toooo long to write here but in a nut shell... neighbors lil truck, cycle the switch in starting once and if it didn't start, no second chance until she would get back out, rock the body on the wheels and back in to try starting again. This was common practice for over 2 years. All she really needed to do was open and close the door. We still laugh about it.