[Paul’s clock!]

Hi, I now have my uncles old Smith Sentric 24” clock which I wired in. Power has been switched off numerous times due to working on the system. I’ve pushed the bottom knob in adjust the time and restart. The last time the knob didn’t seem to engage, and didn’t feel right. I could adjust the hands but the clock wouldn’t start. I couldn’t hear the motor humming but there was a slight vibration from the mechanism. I have stripped the clock down and found a broken piece (photo 2). I don’t really know how these clocks function but suspect the bit concerned links to a small part with teeth which engages to the motor drive spindle. The broken off piece I also believe sits between two washers (photo 3) at the top end of the hand adjusting rod. When the nob is pushed the once intact piece would engage with the (photo 4) arm that connects to restart the motor.
Am I on the right track, and is there anywhere I can pick up a replacement for the broken part? Local clock repairers have just said replace the mechanism with a quartz’s. This will only happen as a last resort!! Any help would be much appreciated. Thanks.