I continue to examine real moon phases and star movement shifts with great interest and am giving you my results. For the moment, I notice + or - 10° shift between expected star positions, corresponding to 24 minutes (180° = 12 hours). But this figure is not totally sure because I have no real tool for mesures. You can use the North Star as fix point and a visual hypothetic line rising from it and directed to the North Pole. Then stay at the same place and look at a big star position compared with the line position. With software, you may see where the star is expected to be at the time of your observation and compare the both. Then 1º shift is equal to 2.4 minutes. I think it's a good and easy way to measure time shift with stars.
Offered by H.