Just went through this on an '04 and this thread was helpful, thanks Ian for pointing out where it was.
Thought I would post some pics to help those in the future.
I was getting a code 25, which is the "seat position sensor" code.
Since this is under the seat the repair involves removing the seat, no other panels.
Basically I put the seat in the middle position so I could get to the bolts easily, tilted the back part of the seat forward some, then I disconnected the battery to be safe and unbolted the 4 14mm bolts holding the seats.
Then the seat is pretty much free, and the wires are long enough to tilt the whole seat back against the back seat (tilting the seat forward helps here). Then I could easily see and reach everything on the bottom.
Peeling back the covers you can see why the light is on all the time.
To get more slack to repair the wire harness I unbolted the seat belt buckle, its one 14mm bolt and fish that under the seat and then its easier to get to the wires, but not necessary.
The broken wire was so short, I got a spare pin/wire off an old gs300 harnesses (you can find type of this pin on most toyota harnesses), and soldered and heatshrinked it in a little longer than the original.
The end result with extra split looming over it just because.
Connected battery and inserted key and now the light goes off like normal. No reset was needed, it resets and checks for faults every time the key is removed and put back to "on" position. I know that because sometimes I would get it and sometimes I wouldn't when the wire was probably on its last strands.
Its a pretty easy fix and there is no need to replace the floor harness behind the dash it seems, at least for this issue.
This harness branches off of the seatbelt harness which is hardwired to the seatbelt mechanism and plugs in under the seat in 2 places, so getting a new seat belt mechanism w/ harness would probably work as well if you don't like to repair wire.