Black valve leaks

The quick way to try
Is get the add on drain back flush attachment
The clear one with the hose attachment
I never had clogging or dripping problem
When I used one of those on my RV
I can't use it on this RV with out making some mod ,
It's a clearance problem in the compartment

They do make a valve that you can attach to the existing valve thus you have 2 valves in line. I carry one as a quick fix if I have a leaking valve and do not wish to try to fix the original valve on the road.

I think this is the add on valve

Very common on black tank valve to get a piece of tissue stuck in the blade of the valve. Usually requires taking the valve apart and simply cleaning the channel that the blade seats into. That age trailer should not require a replacement.

I have been able on occasion to completely fill the black tank with fresh water and flush out the debris.

Is this a remote valve with a flexible cable to it?

Replacement is likely, but sometimes this old trick will work. After empting the tank run clean water into it either with a hose or via a tank cleaner.

As the tank is draining clean water work the slide back and forth several times. Sometimes all that action will dislodge what is stuck and it will wash out.

You could try running a lot of water through it...but replacement is likely in your future.