Rusty-
There are no dumb questions...just dumb people. kidding!!!!

I just got done giving the distributor on my 54' a "once-over". I'm not sure if it will be any different for your 60' engine, but if you look here:
http://chevy.oldcarmanualproject.com/shop/1954truck/54ctsm0009.htmlLubrication point number 8 talks about the distributor cup (or Grease Cup). The CL in the circle stands for Chasis Lubricant.
When I took mine off, I removed the entire unit (cap and the part that actually screws into the dist), it looked like it was filled with dirt...(50+ year old grease)
After a good cleaning of the distributor cup and that hole in the distributor that it screws into (make sure not to lose the spring and fibre plug that contacts the dist shaft).
good view here, #'s 2,3 &4:
http://chevy.oldcarmanualproject.com/shop/1954truck/54ctsm1229.htmlI simply un-screwed the top, and filled it with grease out of my grease gun, not sure what type, but try to make sure that there aren't any air voids. I put the cap back on and tightened it down just far enough that the threads engaged and grease was coming out the end. Then I re-installed the fibre plug, spring, filled the hole mostly full with grease, and re-installed the distributor cup.
After that, just give 'er a turn ever 1000 miles & you're good!
Hope this helps