I had this same issue on one of my Ballys.  With the flipper button depressed, a bit of finger pressure on the tip of the flipper would cause the "chatter".  I dug a bit into the web, and the solution (at least in my case) was replacing the coil stop.

If you simply change the coil stop with a coil stop in the game from another coil (try the other flipper's coil stop), see if that fixes it.  Coil stops become magnetised (and mutilated) over the long haul from the constant hammering.

+1

A flipper kit would solve all the issues. I'll bet the original flipper parts have had a hard time over the years ! You can file and adjust the EOS to reduce the chatter, but it will occur again if the original, worn out parts are still installed.