I'd been using the BT units with a mono TS cable for output to the radio and/or amp. This meant that I was (supposedly) only hearing L-channel audio output. So I decided to make up a stereo-to-mono mixer box to do things properly, to get mixed L & R channel audio out.
With the mixer in place, I played a channel identification setup track and got both L & R channels, mixed to mono, as expected. So all good. Then I disconnected the R channel input from the mixer and ran the track again - and I still heard both L & R audio! So I then re-ran the test with R channel only, and again got both L & R audio. Then, I repeated everything with the other BT box, with same results.
Finally, I put the same channel ID track on a CD-R and used a CD player as my audio source, repeating all the same tests. As expected, when L was disconnected, I only heard R audio, and vice-versa.
Beyond a doubt, both BT boxes are outputting mixed L & R mono.