65 cuda 4speed

My 64 Barracuda used to do that, but I can't remember what it was. Just start looking at all the pieces from the pedal to the adjuster rod that goes through he arm going into the bell housing. Compare them to the Brewers online catalog. You can also take it all apart and clean and grease everything. Check your parts for any cracks or anything bent. Then it would be a good time to replace the bushings and clips. You might want to remove the bottom cover and check what clutch is in there.
Don't know how to do that, although I'm sure it's pretty good advice. But when you say grease everything with what? Like we use grease at work on the wreckers and rollbacks to lube the beds and the wheel lifts it's thick nasty **** you wanna use gloves when you put it on throw em away when your done. Or do you mean like white silicone or wd 40