Echoing what 93celicaconv said, i'd check out a few things before digging into the ecu wiring.
I suggest making sure:
the starter is actually getting 12v on its big lug.
the battery is actually outputting 12v. Made that mistake myself a long time ago, never again.
the battery terminal connectors themselves are in good shape. There's a thread on this forum where someone said their gt swap couldn't spin the starter because the factory st182 battery terminals weren't beefy enough.
the starter is actually good by bridging it.
If all that checks out, next thing I'd do is look at the key barrel and make sure it's getting 12v and sending out 12v when you turn the key to crank it.
*caveat* on the st185's, there's a starter switch on the clutch pedal that has to be closed in order for the starter relay to energize. I don't think you'll be able to trace 12v from the key barrel all the way to the starter enable spade connector unless both the relay and the clutch switch are closed.
Take this if you don't have it yet: http://gt4.mwp.id.au/Toyota%20Manuals/T ... iagram.pdf
good luck! keep us updated. I think you should be able to track this down if you can trace 12v all the way thru the system and carefully bypass items to rule them out as needed. Multimeter is going to be your best friend here.