My '88 recently had the problem. Lucky thing was I had enough tools to fix in
the field while road-tripping in the Finger Lakes. I pushed in the trip meter
reset button, and something didn't sound right. After that - no odometer. I
tore into the instrument panel, and saw a worm gear (light green color) that
had moved out of position from it's mating spur gear. The gear was in the
correct position on its' shaft, but the entire shaft had moved outbound about
1/4". I had to strike it gently with a small socket, and an improvised hammer
(a rock). If it happens again, I will super-glue a shim in place to keep the
shaft from moving, but 3K miles - and SFSG. I now use a kinder, gentler hand
on the reset button.