Extracting Steering Vectors from J space

I was reading about the jacobian space and how it can be used to verbalize the intermediate activations of an LLM to decode what it is most likely going to say or is thinking about. I wanted to test if we can use the j lens to arrive at a general activation steering vector from a couple of tokens related to the concept towards which we wanted to steer the model i.e inverting the j lens to have a general method of finding steering vectors from the concept tokens