@jespah,
My grandfather's alzheimers was similar: put him in a room of grandchildren playing and he smiled and spoke. He'd sing them the little songs he sang to us when we were young. He loved to hold a baby, so careful and so loving.
Otherwise he seemed very unhappy and agitated and seemed to recognize no one.
Though one time when my grandmother walked past him in the living room, he smiled and winked at me and said clearly, "That's some hotsy totsy!"
My parents kept him at home until just a few weeks before he died and I sat with him as he passed. It reminded me of one of Laurie Anderson's lyrics - that when her father died, she felt like a library burnt down. He lived almost the complete 20th century and I did not get enough of his history.
I believe Lady Gaga added years and zest to Tony Bennett's life. There was chemistry between them and Lady Gaga showed a lot of love and interest in him. I believe it when as you said, when she wasn't there, his lights dimmed significantly. Bless Tony Bennett, bless Gaga.