I have finalized my suggested alternative "No Cut" solution.
Behind the driver's side kick-panel lurks connector LA2.
1) Disconnect the battery.
2) Remove the kick panel.
3) Disconnect LA2. See FJ Wiring Diagram for location.
4) Isolate Pin 11 of connector LA2 (refer to page 285 in the FJ Wiring Diagram) on the Differential (female) side of the connection. A small piece of electrical tape works.
5) Short Pin 4 to Pin 11 (page 285 again, male side of the connector, 4 sits on top of 11) with a small piece of bare wire. The friction of the connector will hold the wire in place. This provides the constant +12V to the 4WD ECU. **SEE NOTE**
This doesn't work on all FJs. See SASUVs post further down in this thread for details.
6) Re-assemble and enjoy A-TRAC + RR DIFF without any cutting or permanent modification. To return to stock, just remove the jumper and tape.
NOTES:
1) This may not work if you don't have the trailer towing package since LA2 : Pin 4 is the left tail light power supply for a trailer. Someone without a towing package needs to verify +12V on LA2 : Pin 4.
I'll try to photo-document the procedure this weekend if I have time.
EDIT: PERFORM THIS AT YOUR OWN RISK. UNDERSTAND WHAT YOU ARE DOING BEFORE YOU BEGIN!!!