I discovered a solution that's working for us for now, so I figured I'd share since I know other mothers struggle with twiddling too. I have an old box of nipple shields, and tonight I took one out and handed that to him when he tried to twiddle...he twiddled the shield instead! I can stick my finger inside it and hold it against my covered breast if I need to, but he has been content so far to play with it on his own. I could see a pacifier serving the same purpose, but I don't have any on hand (as one poster did suggest to me).

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I made a big mistake. When DS was tiny and started twiddling, he was gentle and it was cute, and I said "this is no big deal"...so I allowed it.
As he grew older and became less gentle, I disliked it more and more, but he would throw a FIT if I stopped him, or refuse to nurse. So I allowed it to continue. It was annoying but not a huge deal. Whatevs.
Now I'm pregnant, and my nipples are really sensitive. Nursing is not a problem (I think because the nipple itself is pulled so far back into his mouth while nursing so nursing really is putting most of the pressure on my breast tissue itself), but his twiddling drives me UP THE WALLS!
I can't take it. It takes every ounce of willpower not to slap his hand away when I nurse. It's brutal. Not painful, per se...just super overstimulating. TORTURE. Ok...I know I've made my point.

So this is what I have tried thus far:
1. Nursing necklace
2. Tighter shirt
3. "You may nurse, but you may not twiddle. That hurts mommy." Gently moving hand away. Repeat. Repeat. Repeat.
4. Occupy hand with toy
5. Occupy hand with ear/hair/clothes - on DS
6. Hold hands
Nothing works! And he looks so very sad when I stop him.
Please please help. I LOVE nursing DS and would like to continue as long as he has the need/desire, and I am really interested in tandem nursing. I just can't take the twiddling and I need to find a gentle way to stop him that will not impact our nursing relationship (lately if I stop him from twiddling he just won't nurse).
Lastly, and if you've made it this far, thank you so so much, he has been waking very early in the morning now because when I nurse him he wants to twiddle and will wake if I stop him...so it's been a matter of choosing sleep and twiddle-torture, or waking up super early.
Re: (UPDATE) The Twiddling MUST. STOP. NOW.
Elizabeth 5yrs old Jane 3yrs old
Breastfeeding Counselor with Breastfeeding USA
Babywearing Guide ** Newborn Carriers
Cloth Diaper Guide
Safe Bed Sharing Info
Can you somehow completely cover the other nipple? Llike with a thick bra, or a duct tape 'X' (kidding). Put the scratchy side of Velcro or something unpleasant on the other boob so he doesn't want to touch it?
I know it's a bit of a stretch and would need you to get creative to pull it off...but he may naturally choose not to want to touch the other breast if there is no nipple to twiddle?
I tried everything on your list, the only thing that really helped was time. It was awful for a bit, but when I had finally had enough and was consistent in saying, "You may not, that is owie to mommy," and moving his hand, it improved. I won't say it completely eliminated it- he has not nursed in probably 6 months and still tries to reach in my shirt as he's falling asleep, haha- but at 2 the problem is impulse control, not inability to comprehend he's not allowed to do something. Once he figured out I would not allow it, period, he would accept redirection much more easily.
How long have you been trying to redirect him? He may just still be in the phase of "I used to be allowed, maybe if I persist I'll be allowed again!" My only recommendation is consistency.
Hang in there...