You ask, "When I'm in the right seat what can I log"

There is not enough information to answer your question. Being "in the
right seat is irrelevant. If you are still the Pilot in Command then
you log PIC by virtue of being Pilot in Command. If the person in the
left seat is Pilot in Command, and logging PIC, then the situation may
be different. Let us assume that is the case. Is he loggin PIC by
virtue of manipulating the controls or by virtue of being in charge of
the airplane? (acting as PIC). If he he is logging by virtue of
manipulating the controls, then you could log PIC by virtue of being in
charge....but.....the operation of the plane doesn't require two crew
members. So this is iffy, very iffy. You are both logging PIC, and the
plane doesn't require two pilots. HOONNKK! You can't do it.
I don't even think you can log it as Total Time.

Think of it this way, if you log it as PIC and at your airline
interview you get asked, "why did you log these flights as PIC?". What
are you going to say?

The only way I see you could log it as PIC is if you are giving him
instruction, or he is under the hood. Not sure if your company ops
would permit that.