I feel like a dummy
 

Do I need to turn di2 on and off? I've tried googling and I can't seem to find the answer anywhere. I realize this is a really dumb question.

No need to turn it off. Ride it, park it, check battery charge every once in a great while. Done.

I don't imagine it's actually doing anything that requires power if the bike's just sitting there. Battery charge will slowly degrade, as with any battery, but that's about it.

Thanks for the replies, I think it's the only electronic thing I own that doesn't have a power switch lol.

I used to charge mine on the first of each month, then I installed the variant with gear shift position and battery charge indicator, now I
find I can go 3 months between recharges, recharging at the 40% charge level. I put about 200-300 miles per month on each of my bikes with Di2.
Both bikes use the removable batteries which IIRC are smaller than the internal batteries. The oldest is 7 yrs old.

Does it have an on off switch? Or is it switched off by removing the battery.
No on off switch probably means leave it running and it looks after itself.
But if it was running poorly I would swtch it on and off as a first trouble shooting.

When I investigated the SRAM eTap system, it is activated whenever you move the bike but that's because its wifi. They recommend to remove batteries if you transport the bike, not when taking the bike in car to your riding place but interstate or intercontinental travel. With Di2 I believe you don't need to bother at all.