1986 trans am:
when I boiught the car in January, and brought it home, I noticed that the odometer was not working (speedo works fine).

I replaced the gauge cluster with one I found on facebook market place. Again, same issue--everything works in the cluster, except the odometer.

I always thought the odometer and the speedometer were driven together, by the same electrical components.
Why would one work and not the other (on two different gauge clusters)?

 

Probably because the plastic gear that drives the odometer is broken. It's a common problem, do a search.