It is highly debatable whether there is antique bathroom lighting in this old house, or if it is just plain old. It's quite possible that there once was a lovely bathroom light fixture over a mirror. Perhaps there was even a separate ceiling light that was turned on by a push button wall switch.
More likely, the bathroom lighting was minimal to match the house design. Very simple lines and basic, solid building material are the hallmarks of this fixer-upper.
It is clear that whatever lighting fixtures were in the bathroom are long gone. The ugly, bare round halogen bulb and the warming lamp in the rickety old bathroom fan are certainly relics of a more recent upgrade. Investment property owners who buy this type of house just to rent out are not known for antique bathroom lighting maintenance. Instead, this type of landlord is more likely to rip them out and replace with creepy plain low maintenance fixtures.
Mission ahead: find two antique reproduction light fixtures for the bathroom. One will be for over a mirror and the other light will be attached to the ceiling.