If you can jumper the relay and make the pump work, but it won't work "normally", then something's not grounding the relay. The relay is grounded by the EEC when you first turn the key on at EEC boot, then again in cranking position, and finally once the EEC "sees" pip signal, it grounds the relay again. The relay is grounded to turn it on which makes connection between batt and fuel pump. You should have an IRCM which is where the fuel pump relay is, so I assume you've got the IRCM opened up in order to jumper the relay. I've had the trace burn on the IRCM circuit board in the past and that gave me some issues-so if you look close and see a burnt spot on the board, you found your problem.
The bad part about the 2.3L powered cars is that there is VERY little information online for them; most everything is 5.0 related and they are completely different. The 86-89 2.3's had a distributor and were somewhat similar but the later 2.3's were distributorless and had the relays inside the IRCM which is mounted on the passenger strut tower, has a sticker on it with a big letter (N, J, L, etc). I've known people that couldn't figure out why they wouldn't start or the a/c wouldnt' work and scrapped the car because of it; and that little box was all that was wrong with it. That's exactly now I got my '93 coupe. They couldn't figure it out (no fuel pump prime), offered it to me for $400 and I stopped at the junkyard on the way, grabbed an IRCM from a Taurus (and a spare just in case), bolted it on, started the engine and drove it home-277 miles.