Here's an alternative approach, which would work best with two people:
Set up a simple horizontal sundial, with declination lines, correctly
oriented, beside the mirror, say a foot to one side.
Using a laser pointer, or just a bare low-voltage filament lamp, cast a
shadow of the gnomon onto the sundial scale at some chosen hour and
declination.
Move the laser pointer exactly one foot sideways to illuminate the centre of
the mirror.
Mark the position of the spot of light reflected onto the ceiling. This is
the point on the ceiling sundial for the chosen hour and declination.
Repeat for other hours and declinations.
Note that this does not assume that the mirror is horizontal.
Obviously the method could be simplified if declination lines are not wanted
on the ceiling.
Happy New Year!
John Lynes
