You should indeed have B+ constant power at the key switch with the key OFF
This comes directly from the battery ,
So if used your test light at the key switch and nothing at any of the wires solder joints ?
Then your issue is NOT the starter
I never thought or suggested the key switch...
NOT a round connector
THIS , is a NEW JAPAN Ignition Switch for your FJ62
study the BLACK SQUARE / Rectangle Male Connector Plug on the end with the 6 wires going into it ..........
you either left this disconnected or simply have a Blown fuse inside the dash fuse box or out in the engine...
you forgot to plug in your Electrical Ignition Key Switch , the round Rotary Switch , and it has a 18" black cord on it Gloss Loom wrapping up 8 10ga Wires that plug into the
main harness deep under the dash .....