If your alignment shifts with rotation, you aren't polar aligned.
I'm on a pier that is well settled in the ground by now...two years plus. I check it each session (once the pier got accidentally hit by a riding mower). I'm overly fussy, but I figure if I'm going to do it, I'm going to get so close that any variance is probably due to seeing.
I rotate my mount 90° (6 hours RA) East or West. This puts my counterweight shaft parallel to the ground. I start SharpCap Pro polar align tool. When SCPA says "Rotate the Mount", I simply return to Zero position (iOptron CEM60). I then adjust.
Next I rotate RA the opposite direction of the first PA by 90° and run SCPA again. There is invariably a difference as reported by the PA error. That's because, try as I may, my mount isn't perfectly level. So I adjust again.
(As I said, I'm overly fussy and adjust until I'm single digit seconds(") both Up and Down, Right and Left.)
Then I do it all again. The second run-through is usually very quick, since both sides of pier are very close, but one side affects the other (because of earlier mentioned non-levelity [is that even a word???])
After that insanity, I call it good. Others settle for being within minutes, which is fine since guiding will take care of tracking. I just do it this way since it's so infrequent that I need to do it...may as well spend the extra minutes.
When I'm finished, PA doesn't shift in RA or DEC.
Without a pier this would be a total waste of time. But back to your original question, I believe your PA if off if you lose star position alignment when you rotate.
Edited by Dynan, 04 May 2021 - 09:53 PM.