RUN AWAY. RUN AWAY. RUN AWAY. And on your way out, blow the whistle. FAA has an anonymous whistleblower program, I'm sure someone will have already mentioned this.
Although JohnBurke does bring up a good point: if you're manifested as a passenger, don't have a 135.293/297 check...then you might not be in any sort of regulatory danger.
If the company is just paying you to look pretty and that's all you're technically qualified to do on that aircraft...then at least you're getting paid to sit and get.
My guess is you're being paid to look pretty in your snazzy uniform. Lots of CE500/King Air/Navajo/Chieftain/421/414 gigs out there pay an "SIC" to sit up front, even though the PIC is single-pilot typed and an SIC is not otherwise required by company ops-spec, the part under which the flight is operating, or ICAO law, in which case you can't log the time.
You are a trained professional. If they choose not to treat you as one, leave. Someone else will.