If the military aircraft does not turn on Mode S (or probably more usually leaves it in standby) then it will not show. There may be areas of airspace that require Mode S to be turned on - then you will see it. If the military aircraft sets emergency on its transponder, then the emergency is automatically sent on all modes - hence the emergency indication seen on Mode S from the F-35. At the end of the day, the presence on the screen for Mode S/squitter depends upon what the aircrew set on their transponder and their emission control instructions.