The tailpiece which the strings tie to. I consider this the most essential item because without it, the strings have nothing to tie to, and thus no sound can be made.
It is possible to make your own using instructions from Shamisen of Japan (link) or this video (link) (Yes, I need to refilm it in higher quality at some point), or you might be able to find a used one at an auction site. But no matter what, the neo is essential for making a shamisen playable.