I had the same problem. A very small diameter drill bit inserted and twisted by hand may clear it. Insert it in the VERY tiny hole indicated by the red arrow in bossee's post. I tested the gauge itself by snipping the cable tie (#32 in the diagram) and using a canned compressed air to blow air up toward the gauge with the key turned on. If you get a speed reading (mine showed 95 MPH !), the clog is definitely somewhere in the tubing inside the lower unit. After doing the drill bit routine, try blowing some air down toward the lower unit through the hose (#33) and see if you can feel air coming out the hole.
Do a search on "Yamaha speedo" ; you'll find several threads about the problem.
Good luck; this seems to be a VERY common problem with the Yammies.