The Captain is always the guy with four stripes.
Even when he is resting.
In my company, when we have 3 or four member crews, we have the figure of the commander. Even when the augmenting crew member is a Captain, the Commander is always the one in charge of the strategic decisions. The Captain or the SFO are only allowed to take tactical decisions.
To take a nap, before crossing the Intertropical zone is of course, unthinkable...