Would you have, as Captain, taken a rest break right before traversing the ITCZ?
Yes, discussed to death; to repeat an earlier response, "no", I never took my rest period during an ITCZ crossing, (A343, Pacific routes, NA - Australia). It was a matter of policy, (mine, not my airline's), not of crewing, trust, or anything else; the cockpit is where "the captain" belongs, in my opinion, as the crossing is an area that presents specific operational challenges and decision-making opportunities, if I can put it that way. The only think I was never entirely happy with was the notion of "RPs", (great guys & gals, but the position is not cleared to fly below cruise levels and therefore the RPs are entirely unpractised in what little manual flight there currently is available - I always thought that was false, short-term economy).
The ITCZ conditions described in the Report are precisely as they are during most crossings. Sometimes deviations were necessary, sometimes not. HF was mostly good but the advent of ADS and especially CPDLC were a god-send for such requests.
The radar would be on, tilt and gain used according to standard operating principles, (scanning up and down, calculating tops of the moisture, gain on automatic as well as manual settings). Sometimes one would have a full moon to help pick one's way between cells and avoid the over-hangs, (where necessary, almost always diverting upwind). While not frequent, St. Elmo's was often seen as was lightning, (which would also help light the way ahead if the build-ups were isolated enough). Light to occasional moderate turbulence was the rule as was the occurence of ice crystals; I know that sound that they make on the windshield.
Some common images, (obviously before nightfall), some of which I have posted before for those who may not see this from the pointy end and are trying to imagine the process of navigating ITCZ weather - it is in my opinion an art as much as it is a technical process:
CPDLC clearance to deviate:
Standard track off-set technique:
The weather deviated around:
Typical ITCZ weather:
At the time, we were informed that aircraft icing never occurred at cruise altitudes, below -40C, and while the problems with pitots and UAS events were occurring then, we never heard a thing about them and never once were shown or practiced the event in the sim, nor was the info ever presented in annual recurrent training or safety reviews.
I hope this is helpful for those who may not have seen this kind of weather or flown it.