I have a Nikon FG with good batteries, and correct exposure indication.
In manual mode the timing of all the FG manual shutter speeds are controlled by quartz. The eleven speeds from 1 to 1/1000 second are supposed to be timed exactly as you set them.
The problem is that the slow speeds from 1 to 1/30 (red-marked speeds) are correct BUT that ALL faster speeds appear to use the mechanical 1/90 speed.
I suppose that the AE and Program modes will yield the same results.
How are you determining the faster speeds? By audible guesswork or visual timing device?
I apologise if I'm teaching you to suck eggs... The reflex mirror and shutter curtains can only move at a certain maximum speed (the faster shutter speeds are obtained by the second curtain starting to close before the first has fully opened). This could explain why the speeds (1/60 - 1/1000) might sound the same.
In a camera with quartz-timed speeds, the quartz timing applies to manual speed settings only and auto speeds are a separate issue.... so, assuming that you do actually have a manual speed malfunction it does not necessarily follow that you will have the same situation on auto. I would use the TV test in any case to get a quick and fairly accurate idea of where your faster manual speeds are.