That last word “Indoors”is the clue…
The TM-D710GA has a built-in GPS. Not surprisingly, it does not receive indoors, and it has no provisions for an external antenna (only an external GPS receiver).
I had setup the radio for A-side APRS, and B-side Club Repeater (also on 2 meters). Diving into the menus I entered a fixed GPS location and time, since I wasn’t receiving the GPS signal. Try as I might, I could not get a Beacon out of my radio.
Turns out the problem was the lack of GPS sync. Turning off GPS resolved the issue, and I now have the radio configured to beacon whenever I press the “BCON” button. Sweet.