Right hand grip (for right handed 10m air rifle): should the pressure from thumb and fingers be equal, or should there be an element of backwards pull into the shoulder?
If we break down the question, and look at thumb/finger and then the backwards pull. Text book shooting should have a grip that is similar to that of holding a hammer (i think it was Heinz who put that). The trigger should be operated using the centre of the first pad of the trigger finger. It should be operated in line with the barrel of the rifle. If the trigger is operated either with a different part of the finger or not in line with the barrel it can deviate the shot as the rifle can be “pushed” off target during the operation. Again text book the trigger should be squeezed between the thumb and finger. most people wrap their thumb around and end up pulling in line with the web, but this is difficult to achieve consistently and effectively with the wrist remaining straight (and we need a straight wrist to reduce interference with the tendons leading to the fingers. the whole hand dynamic changes as well when the wrist is bent, try it for yourself and see what happens!)
Where the rest of the fingers go, is entirely personal preference however you need to consider that they shouldn’t be used to stabilise the gun, they should just sit there! The trigger hand is only there to fire the gun! nothing more. also there shouldn’t be “pressure” on the fingers.
If you are having to stabilise the gun with the trigger hand then there’s a positional issue elsewhere which is usually because the rifle is too long (the backwards pull). When you have a butt that is too long, the trigger hand tries its hardest to hang on (because the grip is too far away to be easily reached. this also inadvertently makes the gun longer as the muscles involved in the upper arm/shoulder contract and become bulkier – its a vicious circle) which in turn leads to excessive gripping, subsequently making it impossible to relax the hand and thus hinders shooting when the gun is moving the least.
If you feel the need for backwards pull because the gun feels front end heavy and the butt plate feels like its not staying in the shoulder right, try playing with some weights to bring the balance back into you.
Check wrist is straight
Check trigger operation is aligned
Check trigger operation is completed with the centre of the first pad on the trigger finger
Check butt isn’t too long
Don’t use excessive pressures that interfere with the hold
Find what works for you