The 99+ trucks have the side air bag feature built into the controller. There was a resistance from the seat(bag or resistor) which you took out. So the air bag system will be disabled until it recognizes the proper resistance.
If you are removing that much wiring, try installing the air bag resistors(2) in the wiring(4 wires) at the controller(right kick panel). If the old seats didn't have side air bags, then the resistors needed are plugged into the seat wiring, just under the back of them. The connectors are yellow, very easy to spot.
Note, the resistors cost a good $15 from Ford, and lots of people have problems with the control module not recognizing the proper resistance. That's in untouched trucks, not modified, just simply the light comes on as it doesn't like the resistance it's seeing.
So you can modify what you have to relocate the resistance to near the control module, maybe play with different resistors etc. But some people haven't been able to fix theirs. If nothing fixes it that way, you might try what I'm going to soon.
I have a 99 Limited with different seats, and three tries with OEM resistors, and two aftermarket sets didn't work. Mine is a rebuilt truck I used for mail delivery. I plan to again soon, and I use it without the right side air bag, sitting on the right side. So I don't need the left air bag much. I'm going to remember some day to hunt a 1998 air bag module, and make that work in my 99 truck. The wiring will be slightly different in the dash no doubt. But I expect that it won't take much work to figure it out, and the side air bag wires will no longer be needed for mine.
