I have this headcanon that Grace, at least once, confronted Stratt and that it is what feed the idea that he is the second in command.
When I say confronted Stratt, I mean "you are a waste of carbon" kind of confrontation, because we love to see Grace and think in a sweet teacher, but, at least in the book, he is a little bit of a infamous diva in the scientific community.
I think it would be even better if Grace does not remember the confrotation at all, leaving it entirely aside as a common discussion or maybe he was just too sleep deprived to remember. And I think that Stratt had to be the one to start this confrontation by belittling Grace for been a Middle School Teacher.
The scene in my mind goes something like:
Stratt in one of her weekly visits to Grace in the lab for him to give her a report in the production of astrophage and Stratt complaining about the progress not going as fast as she was expecting and Grace just explotes.
Stratt : I should have know that a Middle School teacher wouldn't be able to handle something of this magnitude...
Grace (Who has been working no stop for at least three days, have been living in base of cafeine and protein bars for six days, and hasn't feel the sun in at least the double of time): What you gonna do, ah? Fired, me?! Look for someone who replace me?! HA! Good luck finding someone able to do what I do!
Stratt (Quite surprise for Grace's audacity): There are a million of scientists and teachers, you are not special!
Grace (with mad eyes): Maybe that is true, but you are not a SCIENTIST! You may find another microbiologist, damn, you can find an army of microbiologists, but tell me who will explain the science to you, huh? Who would take their precious time to break down a basic concept for scientists into digestible pieces for you?
Grace (Sleep deprived and dehydrated enough to think he can fight god and win): Do you know under which frequency the astrophage is more active? Do you even know how to use the tools required to work with astrophage? Because I DO! You may be all powerful Stratt, but without me you would not be able to distinguish a electron from a proton!
Stratt and the other scientists in the lab:...
Grace (Poking Stratt’s shoulder): Now if that is all, leave and let me work, because while you are giving orders and deadlines as if they are candy, some of us are actually trying to make your IMPOSSIBLE expectations, POSSIBLE!
Grace: And let me tell you that...! Wait! I have it! (Claps to then turn to his microscope) If we use the ultraviolet rays...(Gets lost in his own mind)
The other scientists of the lab snap out of their stupor and crowd around Grace, nodding at Grace discovery.
Grace (Turning to Stratt with a big smile and puppy- eyes, completely forgetting what he was saying before): I figure it out, if we change the rays to a one thousandth of...
Stratt (Still a little bit shaken by the sudden changes of mood): I will leave you to it.
And she turns and leaves.
When some weeks later people question Grace if he is the second in command and he is all "I don't know what gives you that idea", Yáo -who was also present in that confrontation because he was visiting the lab out of curiosity that day- determines that yes, Grace is the second in command.