My '83 GL1100's speedo appears to be mechanical, so after you check the sending unit on the front wheel, check where it connects to the back of the speedo. Both ends look good? Clean, tight (no play side-to-side) and no chunks/dust from what used to be important parts? Cable move easily? Lube anyway...graphite oil or whatever.
I'm interested to hear what you find, since I've got to check all that soon, most likely.