Clicking/Thumping Sound from dash

After feeling around underneath the blower and recreating the problem, I noticed that there is a white plastic vent with a black plastic grate that can be seen if you lay down on the passenger floor mat and look up towards the blower. If you push up firmly on the vent, the clicking noise will stop. I'm not sure if it's a vibration problem or what. I wedged the vent partly closed, and that stopped the noise. I also checked to make sure that when I unwedged the vent after about 10 seconds (when the sound normally stops) that it didn't start back (i.E. I wanted to make sure that I wasn't holding up a motor, which might heat up and cause future problems).

Not a scientific fix, but a fix nonetheless.

I'm having the same exact problem with my 91 Chevy K1500. It has been driving me nutty. I can't believe it is that simple to fix. I figured I would be taking the whole blower out. Now granted I haven't yet tried what you posted but the symptoms sounds the same.