They don't really talk about Snake's past. Snake doesn't bring it up, and Jack doesn't ask, because he's polite. Also because Snake is finally starting to adjust to Jack's dimension, and he seems kind of happy, and Jack doesn't want to mess things up. So Jack just doesn't mention Snake's past, or his old dimension, or anything he thinks might annoy or upset him. That doesn't mean he isn't curious, though.
He's pretty good at keeping his curiosity to himself. Sometimes he catches Snake... dissociating, he thinks. It makes Jack kind of worry... What memory was bad enough that Snake ended up miles away from his own body? Jack never asks, especially since Snake always comes back to himself pretty quickly, but he wants to help. He really does! Helping's what Jack Burton does best, and he cares a lot about Snake. He won't ask, though, because whatever they've got between them works. You're supposed to let sleeping dogs lie, right?
Jack... he kind of slips up one night, though. He and Snake had stopped in a motel room and were sharing a couple beers they'd picked up earlier. Snake was asking questions about Jack's childhood, and Jack was happily chattering away. His school years hadn't been the best so he just glosses over those, talking instead about his mom and the handful of friends he'd had. Eventually Snake stops asking, though, and the silence starts to feel too long and Jack is drunk enough that his curiosity wins over his self control.
"Hey Snake?" Jack leans up on his elbow, Snake still lying on his back on the worn-out motel bed. Snake glances at him.
"What was your life like? I told you all about mine." Jack half shrugs. Snake glances at him again, expression unreadable, before he closes his eye.
"You saw what that place was like."
Jack nods, even though Snake can't see it.
"Was it always like that?"
"What was school like?"
"Boot camp." comes the gruff reply, Snake's brow furrowing slightly.
"Did you join the army right at eighteen? You didn't get to go to college?"
"There was a war to fight. Mandatory draft."
"And then I lost my eye and became a goddamn criminal, yes." Snake opens his eye to glare at Jack. Jack shrinks back a little, unsure of what to do, what to say. He lets the silence stretch for what feels like ages before he sets his beer on the nightstand, turning back to Snake.
"What?" Snake scowls at him. Jack doesn't ask another stupid question- he doesn't even say anything, actually. He just scoots closer, laying his head down on Snake's chest, pulling him a little closer with one arm around his waist.
Snake sighs, letting Jack lay there until he eventually gives in and starts to comb his fingers through Jack's hair.
"Yeah?" Jack glances up, hopeful.
"I had a dog, when I was a kid."
Jack grins, and Snake holds him a little closer, and he tells Jack all about his old dog while the TV plays a western in the background. The tinny speakers filter music into the room, and the soft background noise combined with Snake's voice is enough to put Jack right to sleep. Not that he isn't interested, but he's pretty wiped out and Snake has a really nice voice. It makes him feel safe, same as the rest of Snake, and it's not long before he's snoring on Snake's chest.
Snake lays in silence once he realizes Jack is asleep, still gently petting Jack's hair. He wonders how Jack can feel safe enough around him to just fall asleep like that. Glancing down at Jack, his nose scrunched up as he dreams and a fistful of Snake's shirt held in his hand, Snake decides that Jack's just one of those people you'll never really get. Not that Jack's not open and honest, but that the world never turned him bitter or angry or sad, and Snake doesn't think it ever will. Jack's a weird guy, and sometimes he says the wrong things or doesn't think his actions through, but Snake... Snake really loves him. He doesn't want Jack Burton to change.