I don't know why, but I think that Gaius doesn't really touch people much when he's just getting to know them, but then you kind of are able to tell how much your relationship has progressed by the contact that he makes with you. Back slaps as he passes by, fist bumps for the most serious Shepherds just to push them out of their comfort zone a bit, running his hand through your hair and ruffling it... All signs of affection, even if they just seem like an ordinary thing for him to do.

As for his sweetheart, I think that he wouldn't often go outright and hug or kiss you in public (hey, he's a classy guy once you get past the their bit, so he won't put you too far out of your comfort zone). Rather, he'd have little, sudden gestures, like grabbing your hand and rubbing his thumb over yours in a circle, or pulling you in just that much closer when you're in a crowd. He loves to dash past, plant a quick peck on your cheek, then run off again laughing.