Well I'm leaning towards the relay you swapped might have different internals because if you jumped it with a wire and it works and with the relay in it won't work, I'd say go buy the right relay.
Now about it not shutting off, thats due to the pressure switch. Replace it and the relay too for good measure, and you should get abs working. The computer has nothing to do with the pumps operation, only when to engage the abs to whichever wheels are sliding.
I got a switch for a buick electra 1987 from a buick dealer and it works. It was a lot cheaper than going to Ford for the same switch. The buicks also used a TEVES ABS system. I don't have a part number anymore, but I think if you search here for pressure switch, you can come across some info. I think it cost me around $85.00 and the switch mounts to the pump under the master cylinder resovoir and it takes a special socket to remove it. I think you can use an oil pres. sending unit socket to fit it.
More than likely you'll need to go to a dealer for the switch. I wasn't able to find one at any parts stores.
Also the relay is part number MR-76 according to Auto Zone and is $8.99 I recall it being MR-132 for some reason and having to special order it, but I can't seem to get it to come up with that number anymore so maybe it's been superceded or something.
If you are up to an afternoon job, you could just convert to vacuum boosted power brakes and do away with the abs. It's not too hard to do. And can be done for around $100.00 with parts from a parts store.
You need:
Brake Booster from a 1989 TBird base model
Master cylinder with resovoir from a 1993 Crown Victoria (not the police interceptor)
Then you remove the pump, and master cylinder, install the booster, install the new master, re-use your lines, and run a vacuum source for the booster.
Your lines may be a bit to long so you can either cut and flare them shorter, or just curl them around to make them fit.
Read this and learn all you ever wanted to know about the Ford Teves Mark II ABS System on 89-92 SC's.
http://www.albeedigital.com/supercoupe/articles/abs-system.html
The FORD Shop Manual states that if the Pressure Switch is replaced the Hydraulic Pump Motor Relay should be replaced as well.