They can't keep their hands off each other.
She has decided that she deserves this constant reassurance of his presence after all they had been through, even if some people give them annoyed glares whenever they catch their touching hands or not so discreet kisses. She can't help it, not really. Their hands seem to find each other without realising it, there have been several times when she has gone to get out of the booth and accidentally pulled him out with her, unaware that their hands were linked. It starts as an unconscious need to be close to him, to have a physical reassurance that she hadn't imagined him literally returning from the dead for her; but after a time it became an addiction.
Most of the time they just hold hands. This can be difficult, especially when one of them only has a single hand. They establish this weird dance-like way of approaching things where she uses her free hand for the both of them. Eventually she gets used to just holding his hook, it's easier for them all and she gets used to the comforting coolness of the metal.
If she can't touch him she feels anxious, her eyes scanning the room until she finds him and makes sure that they are at each other's side once again. She knows this isn't healthy, he knows too and keeps trying to bring it up, but for some reason she just can't explain and so finds a way to distract him.
This way usually involves kissing. They do a lot of that.
The pair are often discovered in dark corners with lips swollen and hair out of place. They do try to be discreet, but in Storybrooke there always seems to be someone to interrupt or clear a throat. A sign appears in Granny's back hallway one day, politely asking patrons of the café to be aware that it is a public space and not intended for romantic liaisons. Emma blushes when she sees it, the sign is clearly meant for them, but Killian merely chuckles before suggesting they head home instead? They do take heed of Granny's request for a few weeks, but then Killian smiles at her with that smile over a family dinner at the diner and she completely forgets about every embarrassing interruption they have ever had as her and Killian lock lips passionately next to the juke box. It is Snow who catches them this time, alerting them to her presence with a small giggle and a point to the sign above their heads.
It does wear off to some extent. They no longer have to be in contact at all times, but it still helps when they are. She can go about her day without being constantly on edge with fear that he could just disappear, that Zeus's gift was only temporary, but he always there to greet her when she gets in. She saves up her need to see him, to touch him, until these times alone in their house. Once she is home they do not let go, often falling into bed only a few minutes after she has come through the door. The spend their nights wrapped around each other in love and passion and rest. She can get through the days without him because she knows he will always be there when she needs him.
It doesn't stop them from the occasional make out session at Granny's though.