Villain is a winning and rather tight player. Some 15 players before ITM.

No-Limit Hold'em Tournament, 200/400 Blinds (8 handed) - Hold'em Manager Hand Converter from HandHistoryConverter.com

SB (t12800)
BB (t23120)
UTG (t7223)
UTG+1 (t6246)
MP1 (t8357)
MP2 (t11187)
CO (t10977)
Hero (Button) (t12640)

Hero's M: 21.07

Preflop: Hero is Button with 6, 4
5 folds, Hero bets t900, 1 fold, BB calls t500

Flop: (t2000) 8, 10, 10 (2 players)
BB checks, Hero bets t1160, BB calls t1160

Turn: (t4320) A (2 players)
BB checks, Hero bets t2320, BB calls t2320

River: (t8960) A (2 players)
BB checks

Total pot: t8960
Hero?

It's clear that I can win this hand only by bluff shoving. Doubt he has A since there would have been lead on the river. He might have T, but wouldn't there be raise on turn? If he has T, would he fold on river shove on such board?

I don't think he would lead on the river with an ace. I wouldn't. I think it's far more likely you have random air in this spot than a hand that can call. You are betting 100% of your range on the flop and turn, as evidenced by your actual hand. I'd be checking again and hoping you spewed. I also wouldn't be folding a ten in villain's shoes I think. So I would be waving the white flag here and checking this one back.

Good post by ChrisV, count me in the white flag camp too.

press the autofold button once he c/c turn and is tight.
i expect a turn bet to be very +EV so his range to get to the river is basically Tx or Ax that peeled flop

Seems like a check back in this position is best, villain is never folding to a shove in this spot and has shown that he is more than willing to call your bets.

white flag 100 times outta 100.

Shoving is awful imo.
The hands which you really wanna fold out are 8x and 99, J9 and 77-.
He won't show up with those very often anyways.
I think he'd 3b JJ+ most of the time pre.
So the hands u wanna fold now are pretty much gonna fold to any sizing, so I might bet 1,6 K and hope he doesn't make a stupid hero call with those.
Don't see him getting to the river with KQ/QJ btw.
There's no way u get a T to fold.