PJ2,
The Relief Pilot does not sit in either the LHS or RHS until the aircraft is in the Cruise phase of flight...that would be top-of-climb to top-of-descent.
Not a matter of semantics but there's no *relief pilot*. S/he's a fully qualified F/O and is sometimes called *supernumerary*
Could I ask you to clarify what you mean by "worst times for vigilance"? In my experience, crew-changeover time is (and should be) a routine matter providing thorough briefings are done
It's been observed that a relieving pilot takes some fifteen minutes to half an hour to fully settle into the monitoring / operating routine.
Apparently, if my computations are right - and I have the feeling they are - things started to go haywire just after change-over.
Another aspect of the change-over I haven't raised is about the junior F/O. Supposing that the senior F/O took the first rest slot, that means that the younger started the flight on the RHS (PF or not ) then at the relief point, took over the LHS with very different tasks as PF is by force and by regs the F/O on the RHS.
I have been told by countless pilots that the adaptation is far from obvious.