Cabooses generally did not move from RR to RR. As mentioned, there were some exceptions probably mostly in later years (post steam) that were set up as run through agreements. the reasons were many. In some cases they may not have met all the FRA requirements for interchange. In other cases it may have been state laws that place restrictions on some cars.
My opinion/guess is that up into the 60s or early 70s, cabooses did not show up much off home rails.
The same sort of goes for motive power. I think up into the second generation diesel era, motive power mostly stayed on home rails. The exceptions would be special run through agreements and transfer runs in big terminal areas. An example was the PRR and NYC. There was a coal train that run from Elmira NY, on the PRR Elmira branch to a power plant east of there on the NY Central. They had an agreement in this case that the PRR would handle it one week and the NYC the next. They switched off. When NYC ran it, it had NYC power and caboose and when PRR ran it had PRR power and caboose. I'm sure there were other such agreements.
Another situation was around Chicago. Most major carriers went into Chicago, and to do so crossed the Elgin Joliet, and Eastern RR. Apparently there were many agreements in the 60s and 70s between the EJ&E and other RRs to allow transfer runs - with a caveat. The other RR could bring a freight transfer into across parts of the EJ&E and deliver it to an EJ&E yard. However, the power and caboose had to run back light, just loco and caboose, no cars. Then the EJ&E could do the same and deliver cars to other RR yards, but also had to run back to home rails light.
Run through power and running off hours is a fairly modern practice I think. I don't know when it started but was probably in place by the 1990s at least.
