Isn't it just the stars declination transposed to azimuth? Just guessing here.
For example, if the stars declination is 3 degrees from the pole(-87degrees), then the point it changes direction ( which is due east or west of the celestial pole) would be at 3degrees east or west, so 177degrees and 183 degrees azimuth respectively? (all assuming SCP)
So, again assuming SCP..
Change from left to right(east): Azimuth = 90 - Declination
Change from right to left(west): Azimuth = Declination + 270
Declination as a negative value, eg 90 - -87 = 177 and -87+270 = 183)
Many self-corrections later, I think that is right
Happy to be corrected.