"Last time by" confusion

[TussAgee11]

I was BU so this was described to me by my partner during our post game. It didn't all play out, but lets play along.

R2, 1 out. Fly ball. R2, thinking there are 2 outs, touches 3rd and starts towards home. About 10-15 feet on his way to home (about at the cutout) he realizes his gaffe and takes a few steps (lets call it 2) directly back towards second base across the cutout. The ball is then dropped, and the runner directly advances home safely.

What do you have on appeal?

I've spoken with a few different guys and while we all agree that at some point you have an out in here for failure to touch 3rd on the last time by, we can't really pinpoint at what point he is required to retouch 3rd. By rule, if he "passes" 3rd on his retreat to 2nd, he has to retouch it again. But what does "passes" mean when he never even goes to retouch it? Is there any sort of guideline to be used, or is this just a play you gotta bear down and umpire?