Unscrew it from the wall after removing the mirrors very carefully. Grab a metal brush to brush the loose, chipped paint and rust off and dust out with a old t-shirt or sock. Then lay on top of some cardboard ( I just use a broken down box), grab a can of Rustoleum primer paint and give quick even sprays to the whole inside. DO NOT give a heavy coat, spray a second coat on if necessary but a heavy coat will look runny and ugly).
We had one that looked pretty crappy…so I took a can of white/white spray paint and coated the outer frame and sides of the cabinet.
It didn’t look half bad afterwards.
They are not that expensive. You can get one at Ace Hardware for 20 dollars. If you are going to remove the old one to go through all the trouble of trying to spruce it up, GET A NEW ONE!