Usually you can reveal a Reaction infinite times to the same trigger. Judging from the online implementation, when you react with Tunnel, it is revealed from your discard pile and returned there before the Gold is gained.
Before in a discussion on the forums I argued that Tunnel can only gain one Gold because it is subsequently covered up by Gold, disabling you to reveal it again as it lost track of itself. However, in games with Possession, that Gold may never visit your discard pile...
So, why can't I reveal Tunnel infinite times on a Possession turn? Is that because in Tunnel's case we know it's the same copy? Or is it just Possession being weird?
The weird case is actually Moat rather than Tunnel. Sure it's weird that Tunnel needs to be revealed from a place that cards aren't normally revealed from, and as mentioned maybe "as you discard this" or something would have been clearer, though in practice absolutely no-one ever has trouble correctly resolving Tunnel, so there's that.
"When x happens, do y" means that y happens exactly once per x. When you pass Go, collect $200; you don't get all the money in the bank.
Tunnel happens when you discard it; it happens once per time you discard it. You gain one Gold, not all the Gold in the pile.
In the case of Moat however, the Moat goes back to your hand, and maybe there's another reaction you want to reveal too, oh a Secret Chamber. And we can't see your hand so we let you re-use e.g. the same Secret Chamber. So normally, "when x" creates a window of time for doing things that happen then, and each thing can happen just once, but the Moat family get to happen multiple times.
I have previously cited this as a mistake and still do. I should have done reactions as "when x happens you may play this" (and lived with that killing some while enabling others). They were like that once! I changed them because Moat was weak and there weren't very many reactions. Then Secret Chamber created a situation where we wouldn't know if the card was the same and that's how I ruled it worked.