GerardC, given that the area of weather concerned was probably the only significant one en-route & given the possibility for very severe weather in that area I think it shows lack of imagination to have chosen that moment to leave, having discussed the possibility of turbulence before leaving the flightdeck if I recall.
Some companies produce a schedule of suggested rest allocation to allow each crew.member their allocated due, however this may always be modified at Commanders discretion, & does not nullify his primary responsibility/authority to act to achieve the optimum safety levels.
One would have to suggest that going for his rest just prior to entering the ITCZ weather is neither acting as a Commander, nor utilising much imagination.
What quality of rest did he anyhow hope to achieve back in the bunk whilst getting bounced around, I can't personally imagine feeling very relaxed/rested, or maybe I am just a dinosaur that has seen too many inept attempts to control the aircraft in severe weather & decided I want to be personally involved in weather penetration.( &would, even more so, if I was flying a type with a known history of pitot icing problems)
I am all for CRM, & according trust commensurate with experience, however the one with the 4 stripes should never forget where the buck stops & what he is paid for. . . making Command Decisions. I find no argument to classify this choice to be absent at that moment as one of the better options available.
Easy to be wise after the event I know, but I would wager that a fair percentage of Capt's would hesitate to leave just prior to weather, penetration, in preference to biding their time a little.