I am an MEI/CFII/ATP type rated and authorized jet pilot in Part 135 operation. On the legs where I'm SIC slinging gear and working radios, is it ok to log this time as "dual given" and PIC time as an instructor? Let's assume that I do in fact provide some form of instruction to the other pilot (whether or not this is wanted or needed).
It’s your logbook, so you can write in it anything you want. If a future prospective employer sees somebody doing what you described, the chances of being hired would fall drastically, since nobody in their right mind believes that the FO as PM is providing meaningful or valid “instruction” in a Part 135 or 121 environment to the Captain. If an FAA examiner sees that sort of time claimed as PIC to meet some requirement, I doubt the reception would be any better.
But, you go ahead & do what you want to do, since you will be the one who lives with the consequences. I think it’s a terrible plan, and I couldn’t see wanting to hire somebody who did that, not only because the PIC and Dual Given number are lower than shown, but also because of the brazen duplicity involved.
It’s playing with fire, and potentially risking a one-way ticket OUT of the airline industry. Which, for somebody who would actually do such a thing, would be the better answer.
You're asking two questions here: can you log dual given, and can you log PIC. I assume you already know that you can write anything you want in a logbook; the FAA only cares about it when you use logged time to meet their experience requirements for something. Employers and insurance companies may have their own, different expectations, though.
Anyway, "dual given" isn't defined or required in any regulation so you can log whatever you want for that. Obviously if you later apply for a job that asks for a certain amount of dual given time, you'll have to be able to justify it. I'm not a CFI, but as far as I know most CFIs log dual given only when they also endorse a pilot's logbook to record the training (61.51(h)). Building up a lot of dual given time when there's no record of anyone actually receiving training seems like it would be an invitation for trouble if the FAA or an insurer ever decides to 'audit' you for some reason.
Next, logging PIC time. I guess you're thinking of logging the time per 61.51(e)(3):
A certificated flight instructor may log pilot in command flight time for all flight time while serving as the authorized instructor in an operation if the instructor is rated to act as pilot in command of that aircraft.
It isn't completely clear from what you've said above if you're rated to act as PIC, or just SIC. As far as I understand Part 135 - which isn't much - the operator might have their own OpSpec rules on who can act as PIC. But even if you are rated as PIC, would you also be acting as an "authorized instructor in an operation"? That seems very unlikely, especially considering your comment that you might log training given to the other pilot "whether or not this is wanted or needed". Unless you have specific authorization from the operator (your employer, I assume) to instruct, then I don't see how you could claim that you meet what the regulations require.
Finally, like others who have responded, I have the feeling that you want to push the boundaries a bit too far here. In particular, if the other pilot neither wants nor needs instruction, how would it even work? Would you just talk at him and then claim you gave him instruction? Instruction that isn't recorded in any logbook apart from your own? For me personally, it just doesn't seem to pass the "could I justify this to an FAA inspector?" test.