Showing down wild players

I tend to pay a lot of attention to betting styles in no-limit.
There is a difference between being aggressive and wild.

Aggressive players tend to bet out strong when they have a playable hand, or at least know that their opponent probably doesn't.
Wild players tend to let loose on any two cards.
Knowing the fine line that separates the two can win money.
In this single table tournament that I recently won, one player had a wild betting style.
Up to this hand, I had sat back quietly folding most hands and just winning twice, mainly on uncalled raises. The players I check down here had a history of wild bets, but was also very sporadic. He had raised earlier with 10/3 off, 7/4 off and J/2 off. He had yet to showdown with any pocket pair or ace. And we were at least 30 hands into the tournament at this point.

On the hand, there were eight players left, I was on the button with 1,405 chips, 4th place. The wild man was under the gun (first to act) with 3,358 chips.

I'm dealt 6s, 4c, a hand I normally trash.
Wild man calls ($20 at this point). Seat 2 (1,722 chips, and a little loose) calls. All fold to me, so I call. Small blind posts and big blind checks for a $100 pot so far.

The flop: 5s, 6h, 5c.
That gave me two pairs, a nice situation, and since there was no pre-flop raising I have to assume that unless a blind hit a 5 or 6, I'm good.
Check. Check. Wild man bets 125. Fold to me.
At this point I know if I call I may be committed to play this hand out to the bitter end. But I also know that more than likely I'm ahead. His betting pattern suggests that. More than likely he actually started with two decent cards (K/Q or J, 10 suited maybe). Plus he hasn't seen me show any cards to this point, so he has no info on me.
Two pairs makes a 125 bet into a 225 pot fairly simple. Call. And everyone else folds making us heads up. Had anyone else stayed, it's likely I would have had to consider giving up the hand. Still, I don't want to play this too aggressively yet, just in case I am right about his hand and he hits and also it will keep me with a tight image.

Ace of clubs. Not a great card for me, but again, I don't figure him for an ace, and I'm pretty much confirmed that when he checks. I opt to check too, just to keep a tight image.
Last card is a 4 of diamonds. It hit my other hole card, but is irrelevant since my two pair are 6s and 5s.

He checks again. If he did have the ace before, he would have definitely bet out by now. But I opt to check again just in the small chance he was slow playing something strong to set me up, and more importantly if he wasn't, to be sure I show the two pair to everyone to somewhat confuse them: Am I really tight? If so, why would I play 6,4 off to begin with, and why would I call a raise with it and not bet late?

Wild man shows j,10 off and I show the winning hand for the 350 pot.

If nothing else, if everyone else at the table was paying attention it showed them not to fear Wild Man's betting. If they notice that it can become a real table assault on one player.