Borrowing from my technique for cutting centered grooves on a table saw, here’s how I make centered mortises without having to find the center first.
I draw a pair of parallel pencil lines along the mortise area, using my index finger as a gauge for setting the pencil line locations. (It doesn’t matter if these guidelines match the final mortise width.) I center my mortising machine chisel over these lines by eye, lock the fence and cut the mortise as usual.
Then I flip the workpiece around to the other face and cut it again. Two rounds of cuts will center the mortise perfectly on the workpiece thickness. No measuring!
– Charles Mak