When do captains and first officer don't have the same VHF/HF frequency tuned in their respective RMP? Thank you
There are a few times when VHF 2 will be used by one and VHF 1 used by the other. VHF 2 is used for 121.5 usually, but when an ATIS or VOLMET needs to be tuned in, the PM will press 'VHF2' which will turn off the 'sel' light and tune in the met frequency. Once the information has been obtained, PM will switch VHF2 back to 121.5 then select VHF 1 again, turning the sel light back on.
As far as talking on different frequencies, one on VHF 1 and one on VHF 2, there are two examples I can think of off the bat: transitioning between Greek and Turkish airspace over Cyprus (neither controller frequency talks to each other because, you know, politics, so PM has to hand the current radio frequency to the PF then the PM needs to contact the other frequency (Greek or Turkish) to let them know when they will be in their airspace and provide altitude and waypoint information). The other one I can think of is a similar setup, but this time the PM is contacting Israel 180 miles before entering their airspace with an ETA, altitude and waypoint information so that, well, they don't get shot down. It rarely lasts more than a couple of minutes.
For all intents and purposes, the sel light is almost always illuminated as both pilots are almost always using the same frequency.