The spindle shafts were indeed a bit sticky. Cleaned them but as expected it does not help what I am experiencing. The unit does not struggle to turn the spindles, the mechanism motor (the one responsible for lifting/rotating the head) seems to want to keep rotating even when it has completed its rotation to a different mode.
The unit will then briefly spin the right spindle and shut off after it struggles. The switches and contacts in the tape mechanism seem ok. It is almost as if there is a logic problem or the motor is being driven incorrectly.
As I said, the mechanical functions seem to work perfectly when the unit has just been turned on. It seems that the problem could be electronic in nature rather than a problem with the transport itself. That said, I am not ruling out that it could be a mechanical issue, it just seems less likely.