Be careful of leaving the bare tubers in the sun as they will dry out. Some eyes do develop on the stems as opposed to the neck or collar.
You don't need to worry about matching a specific tuber with a specific eye - just to have an eye attached to a tuber. Sometimes you have to hope for the best and get in there and divide. It has been suggested on this forum (I think it was Pouchella) to get rid of the least promising tubers first in order to better see what you are dealing with. I find using a razor blade type of utility knife requires less struggling and helps with accuracy.
Since you can see the eyes, I would think you want to plant them into pots using a good quality potting soil such as Miracle Grow. If you cut them today, let the cut heal overnight and pot up tomorrow.

Monet Thank you so much for the help. They are in the sun now so I will get them out. I am looking for newspaper to line my pots with and I think I will use peat instead of the Miracle Grow as I can only find the one with the fertilizer. I have some nice compost I can mix in. The knife I will have to get. You should have seen me yesterday with the loppers! Thanks for the tip of leaving them overnight to heal. Only 4 more boxes and some unlabeled!

Should I cover the eyes as well? Or , just the end where the roots will grow?

I would plant the eyes (and tubers) at the depth that you would when planting out (4-6 inches).
There is really no problem at this point using MG w/ fertilizer. I think MG only comes with fertilizer and/or soil moisture polymers - or something or other. With that said, the peat and compost should work well.
If you do use the razor type utility knife I highly recommend wearing sturdy gloves - especially if you have to go through 4 more boxes.

Good advice on the gloves, monet. PD, I would be less concerned with individual tubers at this point than with hacking the clump into some plantable form of sub-clumps. It sounds like you're overwhelmed trying to find individual tubers, which is why I like to divide in fall.

If you can identify a single tuber with a growing eye, then go for it. If not, split them like Jroot showed, halves or quarters, and hope for the best. They really are pretty tough if you don't mangle them too much. They want to live regardless of what we do to them.

What kind of loppers are you using? I do best with a thin- bladed shears. Google 'fruit secateur' as an example. Thinner than a pruning shears, safer than a knife.

I am using a utility knife and it isn't giving me enough blade. Don't laugh but the loppers I was using are the big ones used for tree limbs! I will go for anything.
Thanks so much both of you. I will do the Google. If I plant the eyes as well as the tubers in pots, I can't understand why some people can do it in 4 inch pots??? Not these tubers.