Is there a specific moment where Damon chose to 'switch on' his humanity?

I don't think it was a specific moment, I think it came back little por little.

Like when he gently stroked Elena's cheek because he missed Katherine (even though JP is trying to make us belive it was because DE had met first)

o when he buried vicky so Stefan wouldn't get in trouble and latter compelled Jeremy to forget about her so he wouldn't be in pain.

I don't recall anything specific happening that made him realize he couldn't stay without humanity.

My theory is that they can block their feelings but at some point those feelings are getting trough the barrier until there is none left.