Since the issue seems to be "forgetting to close it", I wonder about a simple programmed in timer. If the door is open more than 15 minutes, it gets a close command.
I suppose one would need an override for when they wanted it open, perhaps a "leave open 60 minutes", or something.
For me (the OP), it's more an issue of not remembering if I closed it. Splitting hairs, I know, but it's a little different. 99.9+% of the time, I did close it, and turning around a little ways down the road to make sure is a waste of time (but it makes me feel better).
I'm not too big a fan of automatically closing the door after a certain time period. And it does require other considerations (none of which are insurmountable). For example, what if something is blocking the door? My preference along these lines would be to have a camera that I could view remotely so I could see what was going on if/when I decided to close the door remotely. Even then, how do I know if I'm locking my neighbor's dog (or some other animal, I live in a rural area) in my garage? Those are a couple of reasons why "instant, hands-off notification" is important.
I still keep thinking that the easiest solution (from a "use" perspective, not necessarily from an implementation perspective), would just be to have an indicator (and preferably a voice announcement) that would tell me as I'm leaving whether or not the door is open while I'm still in range. As I got out of range, the indicator/announcement would stop. I think a wireless relay mounted in the car and triggered by a sensor on the garage door (via Elk or CQC) is an easy solution, but I haven't been able to find a voice annunciation device that would work.
Ira