There is very little info on this, unfortunately. What I can say is that the paint was often the only finish. These paints were most often hide glue or blood mixed with pigments like charcoal, ocre, clay, etc..
I will look for more info. I've wondered about this too but it's easy to take word-of-mouth information and call it good. Archeological studies are best, of course, especially for what you are working on.
Burnishing was also a popular "finish". I have not seen any evidence that burnishing was done in combination with oil or grease. Again, I'll have to check to make sure.