Here is a write-up on how to rebuild your U-Joint and it describes the 2 diameter rivet you take out.
http://wikisho.com/wiki/Rod_shifter_U-joint
The ShoSource solution is you just buy the U-Joint new and put it on (less than $50.00).
If you get an whole different shifter from a member of this forum, it will be in good working order, so you don't have to worry about the quality.
You also don't have to worry about the possibility that something is just plain missing from your existing shifter set-up, and by rebuilding certain sections of the system (like the U-Joint), the missing thing will never come to light (like maybe something is missing that allows your handle to do odd things).
Run a "wanted to buy" ad, if you don't like the prices of the shifter assembly, you don't have to buy one.