I am sorry you are in this situation but I really don't believe he can't find anything to do.
He could fix up something in the house, make a nice dinner, bake a surprise, read the Big Book, watch a movie, excercise, plan his next week, write in a journal/log, call a friend, call AA and arrange for a ride, clean the pantry and remove unused/unwanted items to donate...instead he is choosing to worry you about whether he wants to be sober. And that stinks.