Thanks for the pics George, that helped for sure. I pulled the distributor and opened up the grease cup tonight. All parts are accounted for, cap, body, spring and the disc. The disc looked like it had some life left in it so I'd didn't bother trying to get it out, and I just took out all the old grease. My plan is to pack the grease hole with grease, push the spring in there, pack it some more, load up the grease cup with grease, put on the cap (with some grease in it) and screw it all back in.

Since all the grease cup parts are there I'm wondering what is causing the wobble. I did notice that there was no o-ring on the shaft, and wondered if that could contribute to the wobble? The pics i have seen looks like the o-ring is big enough to offer some support, and thought maybe that is a wobble contributor?

A few questions:
1. Is multi use red bearing grease ok to use
2. Do I need to overfill both the body and the cup cap so that there is enough grease to make it hard to close?
3. Is the concept for greasing to squish more grease into the shaft manually by doing step 2 above (confused as to how grease moves through this thing if the cup isn't overfilled to start?)
4. What diameter and thickness o-ring do I need?
5. With the distributor out, I could only get the shaft to move up and down, not side to side, so maybe #4 is the cause?