my 89 did the same thing and it was a real mystery, the previous owner gave up and took a hot wire from the ignition and ran all the way back to the pump. When I bought it, I spent a couple weeks trying to figure it out. It turned out to be the signal wire for the fuel pump was grounging on the pass. side fender. I lifted up the whole wiring harness leading to the relays and the signal wire leading to the fuel pump relay, with insulation worn out was shorting out on the fender. I propped up the harness with a piece of wood , turned the key and everything was back to normal. Not likey you would have the same strange problem but worth looking at.