I think it was more of a slow change. As the show went on, Peter became more accepting of Kung Fu and slowly developed skills. There are a few moments where he attempts (mystical) things and is then surprised when they work (like heating up an assult rifle in a guard's hands).
The peak of it (I believe) is when Caine and Peter travel back in time and "invent" Kung Fu, where Peter and his father are the dragon and tiger and they fight and Peter actually defeats Caine in the demonstration for the monks.
I don't know too much, I forget a lot. I used to watch the show back in the early-mid 90's, now I just catch the occasional rerun on Showcase once in a while.
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