OK, so Ebbot's Rock wasn't quite the correct place after all.
I'm being wrong a lot in this one, aren't I? Kind of hard that I beat this game with all the characters when I was in college, but it's true.
See, when I went to Ebbot's Rock from Thamasa, I suddenly remembered that there's supposed to be a cave there, and there's no entrance right now. I guess that means I'm going to have to find Strago and/or Realm before I can get to that. And perhaps the key to doing so is getting Shadow back into the party by beating him at the Colosseum on the other side of the map.
To actually fight him, we'll need to bet a weapon called the Striker. It's that dagger we found in the cave on the Veld. From there, we'll have to go to the Colosseum, which is over by where Figaro Castle is at present. It was mentioned before, when we were in the area.
In order to place our bets, we have to talk to the guy at the inside door of the Colosseum. Ask him to explain and he says depending on what you bet, you can get some really good items if the party member you select wins the one-on-one auto battle that takes place against whatever opponent is programmed to be there. If you lose, the item put up as collateral is taken as the entry fee.
For the specific case of Shadow, the item to bet is the Striker, as previously mentioned. I'm not sure it really matters who you have fight him, so long as they're equipped with the best stuff you've got for them. I used Sabin and won easily, in no small part because it seems that Shadow has nothing equipped. Once he goes down, he'll rejoin the party, but say he wants to stick around the Colosseum because the only thing he knows how to do is fight and wants to see how well he does there.
Beyond this one plot-specific thing, I've never really been able to figure out how to make use of this particular element of the game. I know there's some really good stuff to be had here, though perhaps not entirely necessary. Ultros the Octopus is there, at one of the counters, to explain that if you make a bullshit bet, his buddy Chupon will show up and just take it away. I did try that a couple times, but I think in order to actually lose the item the character has to die in the fight, and all I could get Chupon to do is sneeze, which essentially just tosses a party member out of the battle with however much health they have left. Here, it means losing the fight without getting killed, so I still had the items I put up to get in.
I'd have gone on to see if I could actually get Realm and/or Strago next, or some of the other characters, but I've not been feeling well and should really get a little more sleep than I have been, so I'll wrap this up here and just see where things go next.
See you then, folks.