[ There's no reason for him to not walk with her. After all he dragged her here. Judging by the smirk on his face, Damon's obviously pleased she thanked him for the gift.
As they walk, he'll take a casual look at one display case after another before finally stopping at one dated, February of 1892. He's not really focusing his attention on the odd looking device in the case because he's mostly lost in thought. Possibly reminiscing, but it doesn't last for long because soon enough, he starts walking again, moving on to the next seemingly interesting object. ]