Automobile odometer's hands swung back and forth.

If the problem is only what you said, the biggest possibility is that the odometer is faulty.

As far as I know, inside the mechanical speedometer, the pointer tells the magnetic drive of the magnet. When the permanent magnet rotates, its magnetic field lines produce eddy current on the aluminum cover and also produce magnetic field. The magnetic field of the permanent magnet interacts with the magnetic field of the aluminum cover to generate a moment, which makes the aluminum cover rotate against the elastic force of the disc spring, and the pointer is supported by the aluminum cover to rotate at an angle proportional to the rotation speed of the transmission shaft, so as to read the speed value on the dial.

I won't say much about the relevant knowledge. I guess it is caused by the failure of the magnet or the abnormal cooperation between the magnet and the pointer in the area above 80. If there is, what should be repaired can certainly be repaired, but now basically no one will do it, only to replace the assembly. This is a joke. If I have to repair it, the total cost will be 100, and the repair cost will be 100, maybe more.

Of course, I'm just estimating. You can start with a simple examination. The mechanical odometer cable can be easily removed from the gearbox. If there is no problem, please try to replace the new instrument cluster.

If there is no problem, the fault is inside the gearbox, but according to what you said, I can rule out this possibility.