It turns out that position players on a team with ghost players will be rested but only when they have reached the point of utter exhaustion.
These are the four position players on the 23rd:
Hibbard and Macias are down to 17% and 29% respectively. Finally, on the 24th, they get some rest:
It's not realistic to be running players down like this over the course of a long season. If ghost players are to be allowed, simulating a full team, then regular days off for rest need to be simulated as well.
Bear in mind that this is 1903. Stamina is significantly higher and fatigue is lower than present day. I can just imagine how bad this is in a modern league.
One answer, of course, is to stock up with more players and I will be doing that now. However, this ghost player feature seems to need adjustment to simulate player rest as needed. Not that the "real" players don't get fatigued, but that when they do, they are benched for a day in favor of ghost replacements.