"The NCO tool has the necessary parts to repair a spring, the private's tool doesn't. I don't have a clue how to use it, but I know it does."

Yes I know that the NCO tool has the slot to compress a spring so that it can be removed or installed more easily. But a broken spring that is being replaced doesn't need to be compressed. The new spring does.

I am just wondering if the NCO is walking around with a pockets full of Main Springs and sear springs in his pockets to repair a musket on the battlefield?

That is why I think that on the battlefield it was far more expediant to pick up a drop musket from a wounded comrade, or exchange the damage musket with a sargeant in the rear rank, rather that attempt any repairs on the field.

So, with that in mind, I would say that it wouldn't matter a whole lot were the tool was packed either in the Knapsack, or Haversack.