Here's a picture of an old 71C on a test rig.

The gauge in the back is in the main pressure test port. 

The port has a 3/8 NPT pipe plug screwed into it. It may come out easy or may come out real hard, most likely real hard if it's never been out.

You need a test gauge that goes to at least 200 psi and your choice of adapters/couplings/bushings to be able to screw things into the test port.

You don't have to unhook anything else from the transmission, just screw the test rig in and then start the engine

You should see about 135 ish psi with the engine in neutral at idle speed.

If you see nothing or a lot less than 135ish you'll have choices as to what the problem could be.

One choice that everybody in this situation hopes for is that the control valve is bad, since it can be removed pretty easily with the transmission in the boat. you can hope, but chances of it being bad are pretty slim 

Another choice would be the damper plate on the flywheel is shot. That's usually accompanied by loud metallic grinding noises.

And then there's the bad pump choice.

That's a good start to see if you have normal operating pressure before tearing into anything, 

If all was well with the transmission, when you shift to Forward the same gauge will still read the same 135 ish and if the gauge was screwed into the reverse test port at the top front of the transmission in the picture, when you shift to reverse. it will read the same 135ish and in neutral it will read zero. That test port is 1/4 NPT threads and the typical gauge will screw right in.

So, check the main port pressure to start and post the results 

I guess that would fall right into the bad pump (but easy to fix) category  

Since the engine rotation hasn't been mentioned here, you could look at the pictures below and if you have zero pressure, make sure it's indexed the right way.

All of the pictures have to be rotated 90 degrees to the right

First picture is a pump indexed  for reverse rotation

Second picture is a pump indexed for normal rotation

This last picture is also an older style pump (like yours might be since the boat is from the 60's) indexed for Normal Rotation. You'll see a RH after the arrow. You might say that the RH and LH is there strictly to confuse people and make them index the pump wrong thinking that if they have a RH (reverse rotation) engine that the RH should be at the top. 

It confused enough people that Borg Warner eventually deleted the RH and LH stampings 

The best thing you can do is pay attention to the arrow and just plain totally ignore the RH and LH stampings.

http://www.underwoodlaw.net/bw/VelvetDriveInstallationManual-1.pdf" rel="nofollow - link

Just to be sure we're on the same page, if you have the gauge hooked to the reverse test port, you'll have zero pressure in neutral and when you shift to reverse the pressure should go up to the 135ish mentioned earlier. Check that if you haven't already

Then, I'd be pulling the control valve out and looking for anything obvious like a broken spring or a valve that just sorta "fell apart".  It doesn't take long and you've got nothing to lose by doing it.  

And.............good luck 

PS heat is your friend with that test plug

Assuming that you get no pressure at the main test port, swapping the control valves is relatively easy.

Have you verified zero pressure in Reverse like in the quote below, if you have, I wouldn't worry about getting the main test port plug out and just move on to swap control valves  

Then after all that, you'll probably end up pulling the transmission to reindex the pump or just swap transmissions, but there's some hope still that it's a control valve issue.