Okay, I found a 73-75 truck ammeter with a rusty face plate and took it apart.
The 73-75 ammeters are wired up in the trucks the same way as 67-72's and I'm pretty sure the internals are the same too.
Here is what is inside after pulling off the needle and drilling out the rivets holding on the face plate. Basically just a coil of wire wrapped around a plastic form with the pivot shaft in the center:
And here is another view of the internals after taking them out of the case:
Removing the wire coil and the tape underneath reveals this metal "shoe" on the back:
And finally, pulling off the rear half of the plastic coil form allows the pivot shaft to be removed. It's attached to a small disc shaped magnet (2nd in from the left):
When current flows through the coil, it creates a magnetic field that causes the disc shaped magnet to turn (and move the attached needle to one side or the other). The direction of the current determines the direction of needle movement. And the amount of current determines the amount of deflection. Since these meters are wired in parallel with a shunt, the majority of the current flows through the shunt and only a small fraction goes through the meter coil.
When no current is flowing through the coil, the disc shaped magnet aligns with the metal "shoe" on the back (3rd pic) and that is what returns the needle to the center position. Given the way it fits into notches in the plastic coil form and is held fairly tight under the tape & coil windings, it's unlikely that shoe would shift out of position and cause the needle to lean to one side. Also, the pivot shaft appears to be permanently attached to the disc shaped magnet so no chance for unwanted movement there either.
The needle is just a press fit onto the tiny pin-sized pivot shaft. So that seems to be the most likely place for needle mis-alignment to occur. But unless the needle is loose, I don't really have an explanation for why it is now leaning to the left when it used to be centered. Fixing this type of mis-alignment is fairly simple though. Pull the needle off and press it back on so it is centered, being careful not to damage the needle or pivot shaft.