We are a (newly) combination-Paid/Volunteer Rural EMS department. We only has two Full Timers and a hand full of volunteers in a very small town (population 839)
damn.... 839 people, how many calls do you have a year? how big is your station? I'd go nuts from boredom
Disclaimer: I have only worked in urban and suburban EMS systems, so rural isn't something I'm familiar with. And most of my shifts we didn't have defined station chores, other than morning truck checks; we also didn't always have a physical station.
daily chores: equipment check of everything in your ambulance. mechanical check. wash truck if it's dirty.
clean bathrooms, kitchen, vacuum all carpeted areas, and heavily traffic rooms.
fitness - 1 hr fitness during downtime. The camera is kinda creepy (although I understand why they would want a camera, for liability reasons), but if someone wants to stare at you while you are on an exercise bike... i mean, it's not like it doesn't happen at the gym. and you can do a lot of stuff with a TV, a yoga matt, and some free weights.
EMS training - review something. could be an EMS article
Area familiarization / PR: go somewhere public, show the public that you are there, staffed, and ready to go.
Preplan complicated areas with access issues or people with known medical conditions, so it's documented and can be added as a CAD alert.
weekly: check the supply closet to make sure you don't need to order stuff.
deep clean ambulance (empty every compartment, wipe down the insides, clean any mess)
clean out refridgerator
wax ambulance every 3 to 6 months
I'm a fan of giving full time staff more duties than just being on the ambulance, but that also means you can't just hire entry level people with 0 experience right out of school. this can include:
chart review for all charts from the previous week
project review (new equipment)
website/social media/PR campaign
grant research and submission
EMS certification review (make sure no one has expired, or is coming up for renewal)
capital equipment purchases
training developement
inter agency training and coordination
As a general rule, I hate busy work. Giving you work just for the sake of looking busy wastes everyone's time. I don't care if you sleep, provide you have nothing else to do. watch TV. surf the web. spend time on the dumpster fire that is social media. as long as if you get a call, you are out the door in 60 seconds, I really don't care. As a boss. If there is work stuff for you to do, then you are mine for 12-24 hours (depending on your shift), and I can dictate what you do, but I'm not going to waste your time just for the sake of looking busy.
If you are that bored, take a class at the local CC, start a college degree, research a new certification, a new technique/medicine, etc. Be proactive, even if it benefits you and not your agency.