While rock climbing, when crimping a hold, I always use my index finger (and whatever other fingers fit) since I can stack my thumb on top. For two finger pockets is it better to use your index and middle finger or your middle and ring finger (assuming either pair fit).
For the sake of your tendons, it is better to use your ring and middle finger in two finger pockets, because of how your muscles in your forearm insert on your fingers, and how they're wired to your nervous system.
You essentially only have one muscle which acts on all of your fingers, called flexor digitorum profundus. This muscle fans out into four tendons which insert on the distal phalanx (finger-tip bone) of each finger.
You have many other muscles in your hand as well, which also act on your fingers in multiple different ways, but when you're pulling hard on your finger tips, it's flexor digitorum profundous which is getting pumped.
What's interesting is that this muscle is innervated by more than one nerve; the medial aspect is innervated by your ulnar nerve, but your lateral aspect is innervated by your median nerve. You can isolate the intervention of these nerves in your middle and pinky fingers, but your ring finger kinda gets caught in between, It's literally impossible to flex either your middle or pinky fingers at the tips without the ring finger at least partially flexing as well, so it's better to pair your ring finger with your middle and flex them together.
Your ring and middle fingers are typically closer to the same length as well, which tends to make it more comfortable to hold in a pocket, you're also more secure in the hold when you can use your forefinger and small finger to stabilize your hand.
Your angle on the pocket while moving past the hold, as well as its size and shape, may make using your forefinger more appropriate, but for the most part, it's better to grab two finger pockets with your middle and ring fingers.
Demonstrate to people that is it impossible to curl any of the fingers on your hand independently other than you forefinger.
First establish that there is a difference between bending a finger and curling a finger. Bending means you're just bending the finger at the first joint past the knuckle, you aren't engaging the fingertip, curling means you are using both the first and second joints, and engaging the fingertip.
Your ring finger is half innervated by the ulnar nerve, and half innervated by other nerves, so if you curl either finger beside your ring finger, your ring finger will curl at least half-curl, if you curl your ring finger, the fingers on either side of it will half curl, if you curl both your middle and small fingers, your ring finger will curl with them, and there is nothing you can do to stop it (except cheat and only bend your finger instead of curling it). The more force you use, the more your other fingers are going to curl.
While not supported by any hard evidence, in How to Rock Climb by John Long he says
Because it is rate that a pocket will accommodate all of your fingers, the first choice is the strong middle finger, next the ring finger, then the index finger, and so on. Using the middle and ring fingers in a two-finger pocket better balances the load on your hand. The initial tendency is to use the index and middle finger for two-finger pockets. With practice, the middle and ring finger combo is almost always a better option.
I guess there is no definite answer, but will vary from climber to climber, as I saw both methods applied. I use both depending of the angle of the pocket: I use the two finger so that the middle finger is up top. So in a pocket "descending" towards the right I use the middle and ring finger of the right hand or the index and middle finger of the left hand.
Again: This is far from generally true, even as advice I would rather say just try it and go with what feels more solid to you. One great thing about climbing is that every move is unique, both for different climbers and rock.
A practical answer is "whatever works". I've done both (and seen other people do either), and both work fine.
Attempting an "arguably correct" answer from an anatomical point of view is hard. From the point of view of applicable force, it is better to use the index and the middle finger. The reason for that is that each finger has its own superficial flexor, and if you don't consider the rather useless pinkie, they all are not that much different in strength. The flexor digitorum profundus, on the other hand, has two bellies and two tendons. One for the index finger, and one for all other fingers together (which is the reason why ShemSeger's party trick works, has nothing to do with the ulnar nerve).
Thus, not using the index finger means not using half of the available force of the strongest flexor in your hand.
On the other hand side, there is tactile sense which may also be important for climbing. The median nerve lies below the retinaculum whereas the ulnar nerve lies above it. That would consequently mean that the ulnar nerve is arguably compressed less when holding with great force (if you climb "properly" you should not usually hang with your entire body weight on two fingers, though). Less compression means it takes a longer time before you lose the tactile sense.
This would suggest that it may be better to use middle and ring finger together.
So... either way has advantages and disadvantages, use what works best. Both alternatingly if you like.
I personally think it depends on the move and the hold.
Ring and middle finger is preferable for deep monos which is straightforward and downward loaded.
However, if the hold is somewhat an uneven pocket, tilts to an angle or is a mono-gaston move on incline, sometimes its better to use your index and middle finger instead. This is especially true if the mono has a side edge which can be used to press your thumb against. Also note that your are generally much stronger in your index than in your ring finger.