I know this thread is old but....
I had the same problem with that device, only in reverse.....
when I don't crank the engine I have a delay....when I do crank the engine, no delay at all. I contacted David and he suggested I put a 1000mfd 13VDC capcitor in parallel with the input line and ground. When I cranked the engine for the first time after installing the cap I didn't have a delay, but since then it seems to work.
In hindsight I wish I would have built my own delay...alot cheaper and probably would have worked better. Here's a good one:
http://555-timer.clarkson-uk.com/operation/frames3.html