Having mde sure the leak is not brake fluid, then you should replace the axle seals. This is a common replacement, especially in our 40+ year old vehicles. Personally, I go to my local NAPA, but, wherever you go, you are looking for Axel seals. They metal rings with a rubber ring seal. If you are handy at all around your car you can remove and install them. By all means R&R both sides, document the work and move on. You will need to remove the axles , disconnect the brake line ate the wheel cylinder, and rmv the backing plates. The seals are lightly pressed into the opening of the axle housing. Remove them, noting how they are installed, by whatever, means, then clean the recesses. I use a large socket, about the same dia. as the seal. I, gently, tap them back into position. I smear a little wheel bearing grease around the rubber lip seal before inserting the axle, making sure not to damage the seal with mishandling the axle. Once the axles are in place, you can finish the install. You will need to bleed the rear brakes, starting with the passenger then finish with the driver's side.
Good luck!