It sounds like what is being described is a "cruise captain" role, with the SIC acting as the PIC, and signing the logbook accordingly, applicable to the time in that role enroute. The FAA's position is that the person designated by the operator as pilot in command will remain pilot in command for the duration of the flight, and in most circumstances, that will be one person. There is nothing that can preclude the company designating more than one pilot in command on the flight release, however, and as such, both constitute a designated pilot in command. In such a case, the F/O is indeed "signing for the jet" and is the designated PIC for that portion of the flight, and is recognized that way by the operator.

Discussions about logging time goes far afield when talking about filling out logbooks, as it's no longer a legitimate discussion about logging time...that's a regulatory question. However, in the context of what employers want to see, the general US-based answer is that PIC time is applicable to the person designated as a captain, and who is designated as the pilot in command of the flight, and who signs the logbook as the PIC. In that context, an operator which uses the F/O as a "cruise captain" and does designate the F/O (PIC type-rated) as PIC, and requires the F/O to sign the logbook accordingly, makes a strong case for recording that as PIC time (only in the context of stipulating time on a job application).

While the FAA Chief Legal Counsel has established that a SIC acting as sole manipulator does meet the legal definition of PIC for logging purposes, in this industry, in the US, that behavior won't fly, and an applicant is expected to know this.

The pilot in the bunk is still a part of the crew, and is still liable for anything that happens during that flight, as part of the crew, will still complete an ASAP report along with the crew if something occurs, and still has his or her block time count toward flight time limitations. The fact that the total block time counts toward his or her flight time limitations should be noted. One can be liable for flight time, actions occurring during flight time, and for the legal ramifications of all block time, and yet not log it? Not so.

How to log augmented time. One is part of the crew, correct? One is assigned to flight duties on that flight, designated in that role, and performing those duties, and responsible and accountable for that time, correct? (both are correct: it's rhetorical)

Log accordingly.

The regulation spells out logging flight time, quite clearly. Making up categories of time is idiotic. SIC-in-the-lav-while-reading-Stephen-King is not actually a category of time to put in one's logbook. Neither is F/O-in-left-seat-in-cruise-while-touching-the-yoke a shade of PIC. No need to make things up. It's quite acceptable to log less than what one is legally allowed (employers do not care to see you conflate SIC time as PIC because you touched the controls). Adding to it is not acceptable, and making up all manner of categories to re-define your experience is not necessary. It makes one appear like one doesn't understand logging time. It looks more like...padding.