Each ML model, LLM and otherwise, is a combination of matmul operations & nonlinear activation functions on static weights. My understanding of your "ignoring training data" is to change the vector values of the neural network, which is part of what happens during fine tuning.
Curious why telling an LLM to speak like a character, then using few shot examples to anchor the model in a certain personality/tone doesn't suffice? Is it really the training data (meaning the response strays to random nonsense) or is it that the instructions are not good enough?