Every day (00.00-23.59 CE(S)T) when you board a train, no matter when you leave the train, is a travel day, so if you travel over midnight, but don't board a new train that day, then it's 1 travel day.

The only trains I can think of that follow such a schedule are internal DB=Germany ICE trains (=normal daytime trains, seats only, the bistro will be closed nighttime) from either around FRAnkfurt or Rhein/Ruhr=KÖln. REServ on these trains is optional, probably advisable for peace of mind, and is for 4,50 easy to do via bahn.com - seat only - IF you are in DE=Germany, like I am now, then you can even do it on the ticket machines (no crd cd needed then).

I´ve used such trains several times on a pass and never had probs with the checks the next day.