Incidentally, it is my understanding that a implicit contract does exist, regardless of the lack of signatures, due to the fact that you continue to show up for work every day in good faith, and they continue to pay you at the end of the month (including flying pay), thus establishing a previous course of conduct.
I think it's more likely that your attestment/commissioning papers saw you sign-up to military law, which includes stuff like 'following all legal orders' (or words to that effect), such as devolved power to subordinate commanders to issue shift rosters/working hours through section orders.
You don't show-up to work because of a contract; you do so to avoid getting jailed.
p.s. ditto what uncle peter says - lots of people talk the talk...