Is there a word or phrase that expresses the action of "a person thinking about what another person is doing when the other person is not around". For example, John is sitting in his room in Kentucky, thinking about what his girlfriend was doing in Texas.
vicariously means experiencing through others.
vicarious: felt or enjoyed through imagined participation in the experience of others: a vicarious thrill.
I would say he is preoccupied (by thoughts of her).
He has a preoccupation (with her). Or, she is his preoccupation.
"Obsessed/obsession" are used similarly, but they sound a bit stronger than what you described.