The missing cover will only allow dirt to get into the bevel gears.
What has probably happened is that one or more small internal brass bushings have fallen out of position which allows the drive shafts for the odometer wheels to become disengaged.
I suggest that you remove the speedometer assembly, take the stamped cover off of the assembly by first removing the plated front cover, then remove the black case cover, and reinstall the loose bushing(s). They can be carefully retained in position with model airplane "CA" glue. I would lubricate the assembly before you put it back together. Gar Williams