These kind of remote controled radios were common in Germany.
Philips, Grundig and the best, SABA (1954 - ~1965) made them:
all functions by cable remote:
https://www.youtube.com/watch?v=rrxE-v8ZbeU
https://www.youtube.com/watch?v=hvRgOqiGq3Q
https://www.youtube.com/watch?v=Stq33jkglik
https://www.youtube.com/watch?v=gExk47SWCTQ
https://www.youtube.com/watch?v=5i9SWUeLZFI
https://www.youtube.com/watch?v=dLwSjamc0wQ
https://www.youtube.com/watch?v=Q-2MKJzj-Sc
WITH CABLE REMOTE:
https://www.youtube.com/watch?v=nd6Vfm3O8T4
WITH CABLE REMOTE (from Italy):
https://www.youtube.com/watch?v=4a6PJTGue-M
WITH CABLE REMOTE:
https://www.youtube.com/watch?v=dikSHNyUJVs
https://www.youtube.com/watch?v=myovCzawl34
SABA made in 1937 their first motorized radio:
https://www.youtube.com/watch?v=t7OQmmXk_fw
The SABA automatic series has mostly 2 motors, one for the station search
and one for the volume control.
Wave band and sound switch goes with relays.
There was a Tonfunk radio with on/off switch by a supersonic remote.
Just german engeneering!
Regards,
TV-collector