Distributor question

[Bob from Northport]

We have a high point 1930 Roadster in the shop. Getting difficult to start.
The distributor cam/rotor can be moved back and forth about 1/2" which I think is far too much play. We have checked the timing with a light and it is fine.
Is there excessive wear on the distributor gear?? Or the cam shaft gear that could be causing the timing to change?? With a timing light I can see the timing mark moving back and forth slightly when retarded. Or wear on the timing gears???

Thanks!!