Hi,

My 1978 GT has the same setup.

The odometer has failed from time to time.
Once, it was the driver unit down on the M46 transmission that had a separated housing for an unknown reason. I assume something must have hit it or I damage it when changing out a clutch long before I got myself a car lift.
I used a nylon wire tie and put it back together and it still runs the speed portion today. Still running the second clutch but it’s so aged that’s the splines get sticky. Driving for a few mile and shifting frees it up until it does it again. 44 years has affects from time to time. (:-)

I have torn into the mechanical part of the speedometer head.
Done this a couple times and each time found that the shafts were loose in their respective journals.
So much that they worked themselves apart and we’re jamming.
Sometimes resetting the trip helped or pushing something up under that pin pushed down inside would make it work some more. Lots of wear.
I use a center punch to tag the metal tighter around the worse offending shaft or shafts to make it work for quite awhile but after the second time I decided the odometer part was worn out.
I just didn’t need it or at least the trip odometer.
They have both quit now as one works the other until jam time.

The speedometer portion still works as the cable directly spins the magnet under an aluminum cup.
This setups an Eddy current magnetic field that opposes the direction of the spinning magnet.
This force turns the cup that has the needle attached to it.
A coiled hair spring contains or limits the rotation and thus is the calibration to show speed.

You may not find the same issue as bad if you don’t have over 350k miles on the odometer.
So you might be able to save it by getting things aligned again.

Hope this helps.

Phil