No, the speed sensor drives both and if it were bad they would both be dead.
This is a mechanical failure in the odometer drive, there's a stepper motor which drives some nylon gears, the gears can slip out of line and get stripped.
https://imgur.com/a/kgCLBOO
You can see the stripped gear here, it's the one driven by the worm gear on the stepper motor.
In mine I moved the gear back into place, used a dab of CA glue to try to keep it from sliding sideways on the shaft again, used a small pick to re-form the gear teeth a bit, then added a fresh drop of 3in1 oil. It's been working fine since!