I think the OP has a bad VM or isn't hooked into "clean" power, may be ignition interference.
Does it vary with key on engine off?
A bad connection isn't going to make the VM show 20V on a 12V system.
As for Posi-Taps- I think they are fantastic and have been trouble free for me, used them for years.
Trepidator- Are you sure you aren't thinking of something like ScotchLok squeeze connecors?
(Responding to points in order
Yes, it could be a bad VM, either defective or which responds to noise rather than filtering it out well (as virtually all analog-to-digital converter do which are used for DVMs.)
I got the impression that the wild variation was fleeting, and possibly induced by extra movement. That together with the VM going blank indicates a bad connection somewhere, maybe even within the VM. But the way modern electronic products are made and tested, bad connections within them are rare once they are deemed salable. Seeing a 20V reading transiently during rapid connection and disconnection of power to the VM need not implicate the VM build quality. (It does indicate a scrimping design approach, but so does the $20 retail price.)
I have no specific experience (that I remember) with Posi-Taps. I just know that I've never seen a non-crimp, non-solder wire tapping device that looked reliable in the face of wire size variation, strand count variation, and installation with common hand tools. Maybe my view of such things has been soured by those ScotchLok things. In my years of work, I have come to appreciate reliable connections and despise questionable ones. (That's why I have crimpers and a willingness to solder when needed.)
Until the OP makes some measurements, getting at the cause is a guessing game. Improving the guesses is why I recommend getting and using another volt meter.