As 70herald suggests, take the distributor out. Its very easy to do, just loosen the clamp and unplug the electronics connector.
If you have any significant movement in the shaft (e.g. from bearing wear) you will not be able to get a consistent gap for the electronic pickup, and you'll probably have erratic timing. In fact, if its wobbling a lot, you will see where the pickup has been getting scraped a bit from the rotating reluctor.
Rebuilds are pretty inexpensive. Check out our forum supporting vendors.