What is this that I'm feeling? It's not all the time, it's almost random. Very light taps, you almost have to have a mind for noticing little things to realize it's there.
Could be the exhaust contacting the trans cross member? The exhaust can sag with age, the trans mounts get old, as do the motor mounts.
A quick test is to try and stick your finger tip between the (old) exhaust and the rear of the trans cross brace. If you can't get a finger tip in there, it is likely to be a problem.