Wow, so this is what's it's like to come back onto AFF after doing 12hr/4 sector days for the past week!
Being an SO for 5 years this is my give on it...
I've given a lot advice over the years...still happens on the 737 too. No joke. 
Definitely. Not manipulating the controls leaves extra brain space to pick up on potential threats and errors.
We had landed in AUH on 31R. 31L was closed due to works. I had been to AUH many times in the previous couple of months and had become familiar with the many taxiway/runway closures in progress. It was midnight local time, 7am back in Sydney. So fatigue here was definitely an issue. The instruction was to take a certain taxiway.
Because 31L was closed it was not lit and looked like another taxiway (the taxiways in general in AUH are huge). So the captain crossed 31L thinking he was further along the route than normal. I was sitting in the 'naughty corner' (in the 777 if you're in the seat 4 position you really can't see much out of any of the windows). I had noticed the aircraft started turning left, from the corner I yelled out STOP! The captain stopped and turned to me. I showed him on the chart I think we're here and we need to cross one more taxiway as instructed to get to the gate. The other 3 pilots also checked their charts, concurred with me, the FO double checked with ATC and confirmed we were one taxiway short. Luckily I stopped him early and we could just continue after a slight correction to the gate.
The SO will only communicate with ATC when occupying a control seat. We used to fly 'seat PF'. So if the capt was PF and goes on rest then I become the PF and the FO will do the radios and vice versa. Virgin has this thing that no one shouldn't be doing anything so they get the pilot in the 'naughty corner' to listen in (there is no radio for seat 4 anyway) and write down clearances on the back of the flight plan. The SO in seat 3 would get the ATIS on VHF3 and also contact the company for arrival info.