If the turret is not traveling far enough then that would mean the the computer thinks that it got enough pulses to be in position, when it actually has not reached position and thus is seeing phantom pulses. Since your maintenance staff have pretty much eliminated mechanical issues as a possibility, the most likely cause is electrical.
This can happen with a bad encoder, a loose connection, or electrical noise due to poor shielding. In this case since it's been working for 35 years, worn cables or a bad encoder is a good possibility. An oscilloscope is the easiest way to track this down. Look at the encoder inputs at the computer end. Ideal is a nice crisp 5V square wave, if it is ''fuzzy'' then it's time to dig a bit deeper.
The fact that is seems to go back to normal after a shutdown would indicate that something is heating up over time and goes back to normal after a short shutdown. Maybe a capacitor in the encoder?