Take all relevant and obvious facts into consideration, then make a decision and, if possible, communicate that decision to the Airline. The Duty Ops Officer may have knowledge that the Captain does not possess and be able to alter the decision. Better that way than ask "what shall we do now?" during the middle of the night when inexperienced staff may be on duty. If no contact possible, then carry out that decision and back it up with a written report.
Regarding the Captain being "on rest period" - the designated Captain is always in command, however that command may be delegated temporarily to a relief Captain or a F/O who is qualified by the Airline to occupy the left seat during cruise relief duties. If the Airline does not allow F/Os to occupy the left seat, then legally the Captain may not leave the seat for rest purposes - harsh but true!