I don't have experience with FJ40's and their carbs, but I do on old Chevy's and Studebakers. From what you have described, it appears you have a vacuum leak that is requiring that you dump gobs of fuel in to make it run.
Is this a mechanical fuel pump? It is possible that the diaphragm can no longer hold a vacuum and suck fuel from the tank to the pump.
Do you have an inline fuel filter in the line? If it is between the pump and the tank, it's a problem (unless it is an electric fuel pump). On mechanical diaphragm fuel pumps, the filter must be between the pump and the carb.
Check your hoses between the pump and the tank. If the fuel hose has any holes or cracks, the pump cannot generate a vacuum to pull fuel from the tank to the pump.
So, yes, verify your pump is pumping fuel.
It SHOULD have a strong stream of fuel, not at high pressure, but at decent volume. (max 7 PSI)
If the pump works, then the next possibility is where the intake manifold attaches to the head. If the gaskets there are not sealed, then you MAY be having vacuum leaks there and you A/F ratio is not proper to keep it running unless you're dumping in gobs of fuel.
Look for detached vacuum lines, PCV hoses, bad intake manifold gaskets, and bad carb mount gaskets.
Also need to verify distributor timing as well.
Some of the classic car guys are doing small electric pumps (vane style) at the tank to pre-pressurize the old mechanical pump and to assist with reducing possibility of vapor lock. It is run in conjunction with the mechanical pump. Not MY preferred method but many do this to BandAid the system.