I think Graham started finding his testicles when McCain had to actively leave Congress and live his illness out at home, McCain tweets notwithstanding. I've never understood their connection, especially Graham religiously following McCain's lead and positions like a puppy following their master.
It would seem to me that McCain had some clandestine influence over Graham. I won't speculate further.
I think McCain had something on Graham and now Trump has something on him. He has made a deal and is now doing the right thing. Just my opinion.