In new photos, obtained by the Daily Mail, TS and MH were photographed in the backseat of an SUV that was driving both of them ... apparently, back to her condo in Nashville very early Sunday morning. You can't see too much, but you can certainly make 'em out.

Matty's turning to look at Taylor, who's sitting next to him. Unclear if there's someone else sitting behind them -- but in any case, they're sharing a space back there with their driver up front. No PDA from what we can see ... besides deep stares into each other's eyes.

If they were, in fact, arriving at her Nashville HQ this late at night (around 12:30 AM) as suggested -- ya gotta figure Matty might've spent the night.

BTW, this was taken after her 2nd show of the weekend in Nashville ... where Matty actually performed alongside Tay's opener, Phoebe Bridgers on the fly. His appearance on stage Saturday wasn't previously announced, and came as a surprise to many ... just more evidence he's sorta lingering around, it seems, and ready to hop in at a moment's notice.

Mind you, the dude's not in Taylor's official lineup of openers at all, and has no real reason to be there for his own purposes -- seeing how he doesn't have 1975 shows until June.

Remember, he was spotted in the crowd on Friday ... this on the heels of a report by The Sun that claimed they were head over heels in love and have been dating for 2 months.

Even more videos surfaced of him jamming out to Taylor's set on Saturday too, and now that they seem to be cool with being pictured in the same frame -- which they could've easily avoided -- it would appear to be a sign that they may, in fact, be a thing after all.