I believe F function is a value orientated function that works , operates ,in conjunction with the instincts at the instinctual primary level of minds structure. The value relates to three instinctual functions sense think and feel. Likened to a relay.
The F function could be viewed though the sense instinct lens of a lens that has three filters and is stacked in a way that favours what ever is the fevered or dominant of the three. In this example with in an order sense being the dominant bis , it could be the instinctual component of feel or think as the dominant bias.
All three utilised together with out bis helps manifest intuitions of a spiritual order, this is Gurdjieff's,. Law of three in action.
T I believe is an impersonal critical thinking like logical orientated view. I do not think morels is really linked to the raw nature of the function T
And the same goes for T in relation to what I mentioned about the instinctual level and sense think and feel. And the making of the law of three happen within.
I am not keen on the other parts of your post but.. so be it.