The cassette player testdidn't work. The player has a lid over the cassette, and when it's open everything is shut off.
However, I found a really cheap plastic radio that came free with something. I tried the 9-4 remote next to it and got a clear dull rattling sound coming through the earphones every time I pressed a button.
I had to change the tuning of the radio to a different weak station before the 9-5 existing remote would give an interference sound. In this case it was a faint whine each time I pressed a button. But definitely caused by the remote. Then I tried the new remote and got a similar sound, but a biit louder, possibly due to the new battery. So it seems to be transmitting. But it still won't sync to the car. All I can think of is that it's a 315 one.
Puzzling, unless I'm doing the marrying completely wrong.