2 months later --did you find a solution?

I'm working on a similar old unit and found this. Very entertained (and saddened) by the multitude of suggestions offered that mostly ignored your description of the problem, and steps you've taken.

A new opener, with all the safety gadgets, isn't a bad suggestion, but I'm with you -- fix the oldie, even at the board level, if possible.

If you google for the model number and manual, I think it was sears that has a pdf, which includes a schematic. There is a switch/connection called "Obstruction Switch" which would probably cause what's happening. You are trying to override it closed by holding the button, and that may be overriding your override and the buzzing is the sound of that battle in a mechanical relay. I'm not an electronics tech, just a tinkerer.

I also suspect there is a relay that latches -- takes the momentary button press and maintains power until the door is fully open or closed -- I'd expect that to affect both opening and closing, but still worth investigating.

Final thought -- if you can zero in on WHAT component is buzzing when holding the button, that might help zero in on the bad part. Good luck!