[Peter Ward]

Just so we are clear....with a polar aligned telescope, motion in DEC over a short period can only occur if something is moving the DEC axis.

The RA gear running fast or slow matters not....as it simply cannot drive a telescope in DEC (i.e the 45 degree departure you describe)

Apart from the DEC motor (could be a rogue input from the autoguider) , an imbalance and slipping clutch would also do it. The latter is more common than you'd think, as oil does separate from the bearing grease over time, and ends up on what should be a dry clutch pad. Even with high clutch pressures, the clutch can never be properly locked, and the 'scope may slowly sag to the "heavy" end. Simple fix is to clean the clutch pads with isopropyl.