I don't know the answer to your question, but the way I dealt with tiredness and fatigue were to give up caffeine, going jogging, and watching my diet.
Caffeine makes you alert, but it stays in your system for 8 hours and prevents you from sleeping properly. Caffeine wakes you up, but caffeine during the day prevents you from sleeping properly, so the next day you are tired and need caffeine to get going again and it becomes a bit of a treadmill.
If you need to sleep down-route, I found that caffeine prevented me easily going to sleep in the afternoon for a night flight. Stopping coffee completely, enabled me to sleep at odd times of the day. I stopped caffeinated coffee, and drink tea or just hot water in the cockpit. (Tea also has caffeine but for some reason it is not absorbed as it is with coffee).
It is important to keep fit, because it just is - you need to keep your whole body slim, fit and functioning to give yourself the best chance of staying healthy and fending off disease, such as cancer etc. But sitting for hours making no physical effort is very bad for our health. The human body is very good at saving energy, so we need to "tell" our bodies to keep working: maintaining our organs and muscles at peak performance.
Going to the gym is one way, but the whole gym process can work to prevent us actually doing it ! Having to sign up to a subscription and be a member. Having to book sessions. Having to pack a bag with shower stuff and a change of clothes. Having to drive and park, or travel to the gym. Having to wipe down the equipment after use, etc, etc. It is not surprising that many just can't be bothered.
Jogging on the other hand is really easy. You can just decide to go jogging whenever you want. Put on a decent pair of running trainers and literally jog from your front door. You can go anywhere, even just along the streets (pavements) around your house. I do that, but also along the canal, river, sea front; through the woods, along footpaths, across the common or moorland etc, whatever is there. And when you get back home - straight into your own shower. No booking, no subscription, no bag of shower gear, no traveling, no parking.
And no time is wasted. Whereas a gym visit can easily take a couple of hours overall; jogging from your front door takes just a long as the jogging takes. Only got an hour?, perfect for a 5km jog.
Jogging also allows you to unwind and de-stress after a duty - I go jogging down-route, often when I wake up very early owing to jet-lag after flying in. Super easy to do.
Diet wise, I try to avoid all sugar and salt. Sugar has a similar effect to caffeine but with a much shorter cycle: Snacking on biscuits in the cockpit gives you a sugar rush which perks you up, but then you get a sugar crash. So then you want more sugar. Our bodies convert sugar straight into fat which it stores. Sugar is super dense pure 100% calories and it is really bad for you.
Salt raises our blood pressure over our lifetime, we actually only need a tiny amount of salt per day.
Anyway........Sorry for the really long post - I went off on one there !! Perhaps I need to go for a run, to de-stress a bit !
