Insurance and FAA are two different entities with different requirements. I guess you could keep an "insurance logbook" that includes the time the insurance requires you to be there, but the guidelines for logging that time would be sketchy at best. As far as the FAA is concerned, the requirements to be SIC and log SIC time are spelled out fairly clearly in part 61 and 135. The FAA uses the term "required pilot" in conjunction with the applicable FARs, not insurance requirements.

From 61.51
(f) Logging second-in-command flight time. A person may log second-in-command time only for that flight time during which that person:

(1) Is qualified in accordance with the second-in-command requirements of §61.55 of this part, and occupies a crewmember station in an aircraft that requires more than one pilot by the aircraft's type certificate; or

(2) Holds the appropriate category, class, and instrument rating (if an instrument rating is required for the flight) for the aircraft being flown, and more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is being conducted.


So the two things that dictate whether or not SIC time can be logged are the aircraft's type certificate and/or the regulations the flight is being conducted under. If you reference 61.55, it tells you the requirements for an SIC, which refers you to the applicable parts of 135, 121, or 91K.