The 12th episode from The New Files, "Two in Karuizawa", which focuses on captains Gotoh and Shinobu. While it isn't ship teasey, per se, many of the scenes and much of the dialog that passes between them creates the impression of them being well... you know. For example:
Gotoh: (turns off car radio) "Listening to the news won't do us any good at this point."
Shinobu: (surprised) "That doesn't sound like the information-nut that I know."
Gotoh: (shrugging) "I said "at this point," didn't I?"
Gotoh: "So now we're back where we started."
Gotoh: "Hey, you're thinking about that konnyaku, aren't you?"
Shinobu: "It had occured to me."
Gotoh: "You're not upset are you? It wasn't that bad."
Shinobu: (chiding) "And thanks to that sidetrip, we didn't get out of Karuizawa until late, despite the fact we left the spa so early."
Shinobu: "We never did find any. I wanted to say, "While we're wasting our time here, they're closing the roads!"
Shinobu: (nagging) "If you had just give up on your precious konnyaku and headed straight for Tokyo, we could've been on the Kan'etsu Expressway a long time ago!"
The background music captures the feel of driving on a lonely road during a downpour, while also adding to the "intimacy" of their conversation. As do the moments of Gotoh having Shinobu plot their course, while he acts as chauffeur, interwoven with casual dialouge and Shinobu occasionally chiding Gotoh, with him either placaiting her or just accepting it. All of which makes it easy to imagine what they'd be like as a couple.
They get better as the episode progresses. Such as Gotoh showing concern while sneaking peeks for her twisted ankle, and Shinobu reminding him, twice, to keep his eyes on the road instead of her legs.
Shinobu: (commanding tone) "Eyes front!"
Gotoh: (deadpan) "Haaaiiiii."
Not that it stops him from trying anyway. At one point, he even adjusts the rearview mirror so he can look at her while he's driving. But her woman's intuition kicks in and she catches him (again!), so he puts it back.
After finding a room for the night at a love hotel, and two failed perv attempts later, they agree to terms: he takes the couch, while she takes the bed. Though, in all fairness, she had offered to take the couch, but he wouldn't hear of it. Once the lights are out, and he's certain she's asleep, he gets up and goes over to the bed. Shinobu turns on her side, so he can't see that she's awake. But her expression makes it clear that she's worried, even saddened, that he might try something.
He doesn't. Gotoh remains a gentleman and quietly returns to the couch without incident.
Shinobu is taken aback, albeit touched by this, prompting her to go over to the couch, on her injured ankle. The camera shifts focus on Gotoh's reaction as she kneels at his "bedside" to pick the towel off the floor and drape it across his shoulders. Since his back is turned, she can't see that he's awake, but Gotoh's eyes never leave her hand, until she pulls it away to return to bed. Which leads to a rare when he smiles moment.