Ok, woah. The starting system is way easier than all of that. When I first did my swap I tried to utilize the 1UZ harness and neutral safety switch to get it started but it was to no avail. If your 1UZ is from a SC400 then I can point you in a good direction.
Ok, on the Supra body harness you have a big 22 pin connector called B-1, it is yellow in color (since you are Pre-89). Pin 12 witch is Black-White in color (Black with a White stripe) comes from the Starter Relay and on the 7M would go to the starter through the 7M engine harness, this is the "supply" wire.
On the 1UZ, if its a SC400 then there should be two plugs that end up near the battery, a 8 pin Black in color called EB1 and a 3 pin Black in color called EB2. EB2 is the one you need to worry about, pin one on EB2 is a rather large black wire, this is the "supply" wire to the 1UZ starter.
So this is all just well and good but since the two are so far apart with no wire capable to carry the "signal" to the starter in the 1UZ harness from the dash a new wire must be ran.
In the Supra the starter relay is in the passenger side kick panel (big green relay), on the SC400 the relay is on the drivers side and its "supply" wire is carried through the drivers side fender to pin one on EB2 on the 1UZ engine harness near the battery.
I ran a 10GA wire from Pin 12 on B-1 across the fire wall (in the dash) over to the drivers side kick panel, I then found a clear spot in the metal that was behind the fender and drilled a hole. I threw some paint on the hole and a grommet to avoid corrosion. I then fished a weight down from the factory hole in the engine bay (where the cruise control actuator lived) and pulled the wire up into and through the fender. I then ran the wire to my swap harness witch was connected to Pin 1 on EB2 (see photo below). I'm not trying to tell you this is the only way, but it sure works and retains the factory relay. I also threw some hi-temp nylon corrugated conduit on it to help it survive the engine bay temps, the elements in the fender, and for "looks" in the cabin (even if you cant see it).
Hope this helps.
Here is the swap harness I made, you can see the loan wire, that is Pin 1 on EB2 and that connects to the wire I ran into the cabin to Pin 12 on B-1.