Two things cause the fuel pump to operate. One is the STA contact in ignition switch and ECU (for starting) then once running the AFM "FP" contact closes to run the pump. Difficulty starting is often due to the STA signal not pulling in the circuit opening (CO) relay. My '85 has had this problem for a few years, I just run with the fuel pump test jumper installed.

Simple thing to try, if it helps, that is your problem, if not, its something else.