I've tried unscrewing the part outlined in red below. No dice. Do I just need to remove the whole rod (above the red outline) and replace it?) If so, can anyone point me to instructions for them. I can't see in there. Worried that I'll pull it out and not be able to put it back in.
(The deeper I go in the plumbing the more things I find that there is no modern fitting-part :)
My new assembly replaces the parts outlined in red. the new assembly has a female thread. I am HOPING that the thicker part of the pipe (just above the black "collar" stopper) is screwed onto the pipe above.
However, I cannot unscrew it. There is nothing to get a hold of. It's perfectly round.
I've tried dw40, and let it sit for 20 minutes. No love.
I'll try wacking it with a board in the direction along which it moves in when it screws (perpendicular to the threads per [this answer])