Should be easy enough to do. Point your scope at the celestial pole which is above your horizon. Take an hour-long exposure every month or two. Use your favourite astrometry software to find the centre of the star image arcs. Plot the results in a coordinate system where the start (or centre or end) of each arc is fixed. Precession is ~20 arcsec / year, easily measurable by anyone capable of arcsec precision. Note that this approach neglects the proper motions of the reference stars, which is likely to be accpetable onver the timescale of the project.
I’d try it but my fork-mounted scope can’t be pointed much above +75 Dec. That said, it might be a fun project for another scope which is (a) on an GEM and (b) not used for anything right now.
Thanks for giving me the idea!