Thanks for the replies, gents. I'm set in my ways as far as how I want to mount my garage opener. I've been putting a remote up under my tanks for years, so hard to teach an old dog a new trick.
But, Cormanus, there was a great little nugget in that link you posted:
https://www.youtube.com/watch?v=CQpBUQ-ZSKw
I had seen this video before and think it's hilarious. And it made me realize that I could do this. My wife is permanently working from home, and we converted our spare room to be her office. I ride by her window every day when I leave for work and come home. I could put a remote on her desk, and when I ride past her window, I could honk to make her close the door. When I come home, I can honk to make her open it. She'd just tap a button, easy peasy!
As for the other solutions, here has been my experience:
Remote in pants pocket: Forgot it was there, washed the remote with the pants, rendering it useless
Remote in jacket pocket: Bumped button while getting off the bike, causing door to hit me in head, rendering me useless