I guess most people listen to music or audiobooks or read an actual book (as any CMDR would in that scenario). Personally, I tend to tab out and do some theorycrafting or actually take a break from the game and do something else - for some this is quite immersion breaking, thus all they can do is stare at the screen and hope they don't get bored. Sure, it's about simulating the vast distances and the emptiness of space and I think it is done really well in that regard - but something like that only can be fascinating for some time; it does get old after a while (it's human nature).
So I fully support a feature that would not tempt players to tab out while still have something meaningful to do during that downtime. There is plenty of reading material in-game (codex), but I already went through all of that, so there is nothing to read up on anymore.
Maybe one could think about what real people would do and then try to implement that as a feature, one way or another?
Reading or listening to music are obvious, but what would CMDRs do other than sleeping, eating, etc? Planning ahead, be it plotting routes, maintenance, prepare for the next few days, etc.
For example, if it was possible I would totally plot various routes using the galaxy map and save them so I can load them later when I actually have the time to fly those routes. Being an exploration game, I actually don't understand why a feature like this doesn't exist.
I also wouldn't mind clicking myself through a mini-game that simulates maintenance/repairs, as long as it has an actual impact and isn't just busy-work.
If hacking was part of the game, I would do it during downtime - trying to decrypt files, possibly getting access to classified data; something like this would be great for any CMDR who wants to RP a criminal. You steal a bunch of data or even actual cargo, then have to crack it open. Also, why isn't faking permits a thing (should be extremely difficult though)?
Ship build theorycrafting in-game would be so nice - sure, we have 3rd party tools for this already - but that's what a real CMDR might also do.
Plenty of things that wouldn't just distract from an otherwise semi-boring journey while also adding real purpose (imho).