Have you considered probing?
I don't use switches on any of my machines. For the lathe I use probing for numerous tasks;
populate the tool table, measurements / reverse engineering of turned forms, BUT, most importantly to
locate X axis center of the lathe.
A touch off fixture that is removable / can be re-positioned, easily attached to the lathe bed can be made to do what you want at any time. Thought ...it's just a tool setter and you use the probing feature.
I have found probing to be very accurate; typically 0.0001" or .0002" repeatable.
RICH