It will vary according to the length of the fitting in the Tailstock.
Arbors or drills with "normal" tangs eject earlier than dead centres with blank ends, but no tangs.
For arbors with drawbar tappings, I screw in either a screw in tang, or a short piece of threaded rod.
Fortunately, the exact position causes no problems on my machine, because the Handwheel is graduated, but with a graduated barrel I can understand the concern under some circumstances.
If it is vital, could you not fit a DRO to the Tailstock? It would need a collar clamped to the barrel for the "stem" of the DRO, and tappings for the read head of the DRO. But it would allow the reading to be zeroed at almost any point if a more accurate measurement of depth is needed.
Howard