I like the idea of using the trigger as it ensures that no one accidentally closes the lift while the projector is running. Sometimes it is not readily apparent that the projector is on. That could be catastrophic.
Reading about the trigger in the manual, it looks like the trigger sends a constant 12v signal from the moment the projector is turned on, all the way until 'the projector has finished cooling". I'm assuming that means until the fans die down. I guess maybe the delay timer relay might not be necessary, as JVC seems to have anticipated the use of the trigger with a projector lift. So I guess I'll try it without the delay relay initially, and then add one if it seems like the projector is not cooling enough to ease my concerns.