Interesting question. Will we ever know the answer? Maybe not... not many Planks means not much evidence.
With other cards you can be certain of sheet mates based on two name cards, front ghost shifts, and side-to-side miscuts. You can also make some leaps of moderately high probability based on things like over/under prints on the back (Lash's, berries, etc.), upside down backs with miscuts, and so on. There's none of those (to my knowledge), when it comes to the cards like Plank.
I was looking around and came across two different Planks that are missing color (scrap) and trimmed. One is a Piedmont 150 and virtually absent of all colors other than black, brown and yellow. (
Link to a Heritage listing of this card.)
The other (I believe) is owned by board member Sean (his avatar is this card). This card has a Sweet Caporal 150 Factory 30 back. This one is similar, but adds the (light) blue background. It's still missing much color. (
Link to a Heritage listing of this card.)
After seeing these, I remembered that I had seen a Chance Red Background from mrvster that had a similar washed out appearance. It resembled the Rossman of my avatar, but I knew the backs of those were different. I went back and found a posting of the Chance.
The Chance is missing color, has a lighter blue (but not darker blue) run, trimmed, has scrapbook damage and has a Sweet Cap 150 factory 30 back. The Plank has those same characteristics. Any chance these were from the same sheet... perhaps one that someone took home from the factory, cut up and glued into a scrapbook? Ok, the last part is a stretch, but seriously, any chance they are from the same sheet?