Got everything back in the car, connected, torqued down to spec and ready to test.
Turned the key one click, got check lights and buzzer as expected, turned another click to start engine and got...
It won't turn over in any shift position, let alone in P/N. All the check lights light up (which I don't recall from before), but the starter doesn't run.
Spent the next 4 hours trying to figure out the problem. Found after pulling the pan that the plastic wiper that meets the neutral starter switch makes contact in N, but not in P, so we adjusted the shifter to give proper contact in both positions. We also checked for continuity from the metal part of the wiper to ground (ok) as well as from the NSS to ground when in P or N (ok) and that the outer pins (this is a 3 pin NSS) show continuity when either the central plastic part is depressed (ok) or the central metal sensor is shorted to the housing (ok).
The starter motor is wired correctly (2 cables, one thick, one thin, on two connectors on the starter: one thick, one thin). Checked all ground straps on vehicle, they measure fine.
At this point I'm at a loss as to what the problem might be.
This is a 1980 Torqueflite with standard console shifter & linkage, 3 pin neutral safety switch. It all worked fine when I took it apart to rebuild it, and nothing's changed except that I replaced worn parts and an installed TransGo shift kit (no changes to the rooster comb or wiper though).