What the hell is a T1?
Addressing your question about which finger to use for cuts, the answer is that there is no hard and fast rule. Keep in mind that when cutting a note, your goal is not to produce a melodic note but rather an articulation, i.e. a blip of sound that ornaments the tune for a rhythmic purpose. In other words, a cut is not the same thing as a melodic grace note as used in classical flute playing. Therefore, it need not have any particular pitch, as a grace note would.
To produce the articulation of a cut, then, you can use any finger above the note you are cutting. In other words, if you’re cutting an E you can use any of the three fingers of your left hand (assuming you’re a right-handed player) or the index finger of your right hand. To cut an F#, you have available any of the three left hand fingers, and so forth. Some players will always use the same finger for cutting no matter the note, while others will always cut with the finger right above the note being played (e.g. the right hand index finger for E, the third finger of the left hand for F3, etc.). And some players use a combination of these two approaches. (Of course for the notes A and B you have only one choice, which is to cut with your right hand index finger.)
So what approach should you take, then? Avoid any proscriptions from Larsen or anyone else, and experiment around on your own. Try different fingers and see which one produces the crispest cuts for you, on your instrument and with your anatomy, and then do that. Remember the goal - a crisp, clean rhythmic articulation, not a note - and then do whatever it takes to get there.
This is my big problem with the likes of Larsen. Flute playing, indeed any instrument playing for that matter, is a very physical thing that is tied closely to the player’s anatomy and physical makeup. Flute playing probably moreso than any other instrument, what with the breath, the embouchure and fingering all having direct physical connections. And every flute player’s physical makeup is absolutely unique, so what works for one may not work for another. Thus there can be no hard and fast rules on how to play, yet Larsen has written a book full of them. My advice would be to ditch the book, and instead start listening and practicing. Do what you need to do to get the sound you want. This is not to say that you shouldn’t seek out the advice of other players, either here on C&F or better yet in person. And of course, if you have a teacher nearby take advantage of that. But don’t ever think you can learn anything about how to play the flute from a book!
Apologies for the rant, but it is early on a Monday morning where I’m at. More coffee…