Hey Sonny, small block or big block? I believe in both cases it's similar, but I will be describing a big block (I know them better). The distributor/oil pump gear rides inside a bushing in the block & is turned by a gear on the front of the camshaft. Maybe you need so see "which way the distributor gear wiggles"? For a big block it could be:
1. Distributor/oil pump drive gear worn (pretty common)
2. Gear on cam worn
3. Busing in block worn
4. the shaft itself on the distributor/oil pump gear worn (not very likely)
5. Hex end of the distributor/oil pump gear that goes into the oil pump (common, but now that I think about it, this wouldn't cause the distributor to bounce around).
If you have a big block, I'd suggest changing that distributor/oil pump gear. "up" options would be a brass gear and/or a hardened "hex" tip (2 possible upgrades) & I would suggest at least the hardened hex tip. To replace it:
a. look at what direction the slot in the gear is facing (where distributor fits) and mark its direction somehow (e.g. masking tape on block above distributor hole)
b. reach down in there with some LONG needle nose pliers and pull upwards with a twisting motion to get it out.
c. the replacement gear just drops down in with a twist, but you may need a try or two to line it up with your tape mark. Either direction is OK, meaning the slot in the gear can be "north-south" or "south-north"
d. all of these steps will let you drop the distributor right back in and fire it up immediately (assuming you also marked the distributor/rotor when you took them out).
e. NOTE --> if you don't get the distributor/oil pump drive gear lines up with the slot in the same direction it was before your timing will be WAY off. That "slot" dictates which direction your rotor points.