Having just moved, after packing at least 150 boxes, I am down with the struggle of finding the end of the tape. Even with the cheap plastic dispensers, the tape would sometimes find a way to reunite with itself and hide its edge. Alas, I became pretty adept at finding the leading edge and if caught early, it wasn’t quite as one with the rest of the roll.
Once you find it, fold it back onto itself (to the sticky side) by about 1/4" and do this after every use.