I think Jim has the right idea. The pump does not require priming normally. I just put a new one last week on my 86 when I redid the head gasket and it just needed to crank over for a bit before it fired up.

You can pull the line loose right under the intake manifold, there is a doodad inline right before the pump that you can get to pretty easy to pull the incoming line off. Then pull the line off back at the fuel filter. Stuff the end of an air hose in one end or the other and shoot the crud out of it. Gas and gunk will likely come out of the other end, so you should try to capture that to be environmentally friendly. Then blow into line from the filter to the tank. You'll be blowing junk into the tank but there is the hope that once its loose it can then flow into the filter later instead of clogging you back up. It helps to pull the gas cap off when blowing into the tank as it will build pressure and splash gas back at you, especially on the side of the road when you are blowing air in with your mouth. (Don't ask me how I know)

If it isn't firing up with gas in the carb bowl then you are probably right to think the carb has some issue as well. It should run at idle for a good 30 seconds on a full carb of gas.

The only thing that made me happy about having to redo the head gasket on my 86 was that I could do the fuel pump out in the open. If you end up needing to replace that sucker it is a pain to get to it and get it free. I hope you can get it going without resorting to that. On mine the pump still worked, but it was blowing oil out the breather tube. You should have a rubber hose going down to the motor mount on that side, see if it is dripping oil or fuel out. That will tell you a lot about the condition of the pump itself.