Sounds like the gear is worn. The worm gear on the motor shaft is wearing the gear. If you get a replacement be sure it is softer metal than the motor shaft worm. They were designed to fail as yours has. Which saves the motor shaft worm. Years ago they made aftermarket gears out of steel and they ruined a lot of worms.
Hi pictured are 1964 Riviera prelim. Chassis manual, and parts book. 1990 Reatta service manual and owners manual (no pen). 1990 Reatta know how binder. And 1990 selling binder.
Finally a 1962 body manual.
$10 each. Plus book rate shipping
With a non functioning console as well. That could be my previous 66 with dual quads added and front seats configuration done. Mine was a GS with single 4 bbl and a chrome lid air cleaner. With bench seat
Hi don't remember if my 64 Riv was like my 61 Electra. But it had a sending unit on the master cylinder. Two leads came from that. If they are to route to each brake light look there for an open in that run.
If it is like my 64. And it should be. Remove the panel that surrounds the a/c vent controls and the panel on the radio face. Also the under dash panel above the radio. That will expose the 2 nuts under the radio that need to be removed. Also as you slide out the radio you must remove the antenna lead at the rear or rear of a side. Good luck.