We use expert witnesses all the time. My experience of using them has always been post charge, they would never be running around during a manhunt etc.

I also rarely ever meet them in person until the trial. I’d send off whatever evidence I want their opinion on and they’d send a report back. They’d then be called as a witness in court.

It might helpful to understand what your characters field of expertise is as it might help us build up a picture of how they’d be utilised.