In my opinion, Billy becoming unstuck in time is simply just him having dreams or hallucinations. He is either sleeping, unconscious or on the verge of going into that state every time he “travels” though time.
To show what I mean, when Billy first became unstuck in time, he had been walking for miles in freezing weather and "He was leaning against a tree with his eyes closed. His head was tilted backwards and his nostrils flaring." After that he travelled through several moments in his life then went back to reality.
Another example would be on Pg. 132 when Billy went to bed. He travelled in time to the zoo in Tralfamadore and Montana Wildhack was brought to him as mate from Earth. He woke up the next morning and realized that he had a dream about her.
Those dreams and hallucinations can be explained by his mental state. Billy knows that he was going crazy and that marrying ugly Valencia was one of the symptoms of his disease. Billy’s psychological problems mainly stem from his childhood as he was once thrown into the deep end of a pool by his dad in an attempt to teach how to swim. Later during his life he witnessed the horrors of war and the bombing of beautiful Dresden. This sequence of events led Billy to check himself into a mental hospital after the war. However, the plane crash is the major cause of Billy’s hallucinations. As mentioned by his daughter, Billy only started talking about time travel and the tralfamadorians after his skull got fractured during the plane crash.
