The phrase "a while and though" is not correct and does not make sense in written English.
It seems to be a combination of two separate phrases, "a while" and "though," which can be used in different contexts.
Example: "I haven't seen you in a while, though I hope you're doing well."
Alternatives: "for some time" or "however."
Don't hate me for this, but the affair went on for a while, and though Harrison did split up with his wife when he got back to the US, it was definitely nothing to do with me.
I sat by the water on our deck, then hung out sitting on the beach for a while, and though the sky turned increasingly gray, I didn't mind.
Twilight sticks around for a while, and even though we don't rush we make it back to camp before it's too dark.
I mean, we've been dating for a while, and even though he's not the perfect boyfriend -- don't you roll your eyes at me! You're not! -- um, anyway, even though he's not the perfect boyfriend, we usually get along great.
And so we stayed together for a while and talked, even though all the time there was a strained feeling of suspicion which rather spoilt this Christmas armistice.
It'll take a while and both products continue to evolve, though, so let's just wait and see.
In contrast, she thought Puck's performance of "I'm the Only One" was "the most awkward thing Glee has done in a while, and drags on forever", though she added that Salling sounded "great".
"Is it lead or is it gold?" We sat in the faint light for a while and stared at the bricks, though no Egyptian mysteries unfolded for the moment.
Eventually he left his mother's church and struck out on his own, attending Catholic Mass for a while and then a small Lutheran school, though that was less about religion than discipline.
The same goes for the short-timers: a recent spate of summer soups (strawberry for a while and then corn bisque) tasted as though they'd sprung from the ground.
I was nice to her for a while and gave her sick notes [even though there was no orthopaedic reason].
