So I finished the IRS swap and took it out for a spin. The ABS light was on immediately. I know they're plugged in and routed correctly. Any other reason why they would be on immediately?
One of my sensors went bad without warning and did the exact same thing you described. I believe there is some sort of resistance check at start up and if it fails, you get the light.
I have some I'll sell you. Your best bet is to go to your friendly shop and get them to run a scan to tell you which one is bad. It won't be a standard obd scanner, it's a body module scanner. Then replace the bad one. Mine went bad with no advance warning 8 or so years ago and I replaced it with one I pulled from a car I was parting out and I'm still running the originals from 1999 on the other 3 corners.