This hand comes from a year-old stream of Jason Somerville from a $10/20 8game session he played on PSNJ. Assume no reads.

Predraw: btn raises, Jason 3bets with A7643, btn 4bet caps, Jason calls.
1st draw: 1/1
Flop: Jason checks with K7643, btn bets, Jason calls
2nd draw: 1/1
Turn: Jason checks with T7643, btn bets, Jason calls
3rd draw: 0/0
River: Jason checks, btn checks back with a T8, Jason wins

Questions:
1) What is Jason's best line on the turn? I see the options as bet/pat, check/call/pat, check/raise/pat, and of course check/call/draw. I personally tend to opt towards check/raise/pat if I'm going to pat and have thought check/call/patting seems way to weak and face up, but I think I undervalue this line. Could someone please elaborate on it?
2) Should Jason intend to check/call river?
3) Why did btn pat back with such a weak hand? I suppose this action might help answer Q1 as to why check/call/pat is a reasonable line.

He played it ok, given the straight draw. Maybe he should've drawn to the 76, but if his opponent is the type to pat T8 behind, then there's no need to break a hand that doesn't draw well.

2-7 is very player dependent in HU pots, so it's hard to say much more without some reads. The worst decision is when the BTN pats the T8.

I think his play is really bad. If he is trying to exploit button tendency to bet unimproved then he should CR. Probably he should just lead out.

I'd always lead and pat this once I get here with this type of hand since it's unbreakable. Button can pat behind because he's taken a line that indicates he never has a strong hand. Depending on where Jason's bottom of range is for making this play he might want to check call this river with this exact hand strength but hard to know what to do without knowing the worst hands he's taking this line with.

Aside from that I think drawing two pre would be my preference.

Leading and patting would be standard w an unbreakable T7 in a 1-1 spot.

Checking and patting, if opponent checks behind and draws, balanced by x/r w value hands, lets him check/pat these hands. But that's not what he was doing.

My misreading the HH was a bigger mistake than anything in the actual hand lol, though T8 is too weak to pat behind.

But a ten is a small underdog over the course of two draws, so you would be slightly going uphill against the math on this one, right?

But on the flip side there really is no great line for this hand

Think betting out is fine, but I think the draw underneath is almost too good though even with the gut-shot straight; you can make a #2. And a 9 will beat many of his pat 9s. I bet/pat tens like T8762.

Can't edit anymore but I would just bet out the T7643. Don't think the draw is nearly good enough. But I also bet out bad draws underneath like T8763.