As of 2016, this is STILL a mystery, for I'd neglected to photograph the entire piece, let alone any info on it. Back in 2008, I did a search of the Brooklyn Museum website, and of the then 120 results for wood, found nothing. I'd even looked at Flicker, and its 224 items matching 'Brooklyn' within the Egyptian art pool revealed nada.
Two years later, however, the museum had 411 items for 'wood'. At that time, there was no photo accompanying this description. I'd hoped the following was my item:
Left Fist Holding Folded Cloth
Medium: Wood, plaster, pigment
Dimensions: 6 11/16 x 2 3/8 x 6 13/16 in. (17 x 6 x 17.3 cm)
Collections: Egyptian, Classical, Ancient Near Eastern Art
Accession Number: 37.2041.12E
Credit Line: Charles Edwin Wilbour Fund
Caption: Left Fist Holding Folded Cloth. Wood, plaster, pigment, 6 11/16 x 2 3/8 x 6 13/16 in. (17 x 6 x 17.3 cm). Brooklyn Museum, Charles Edwin Wilbour Fund, 37.2041.12E. Creative Commons-BY-NC
Now there is a photo, taken by a museum curator:
This is a MUMMY cover's hand!
Meanwhile, the cord shows up in the hand of quite a few statues and reliefs. The Metropolitan museum has three examples from the Middle Kingdom, each grasping the folded cloth or rope in his right hand. The only reference I can find to the meaning of the cloth or rope is that it "resembles the hieroglyphic sign for 'health.'" (Eternal Egypt: Masterworks of Ancient Art from the British Museum, by Edna R. Russmann, Thomas Garnet Henry James, British Museum; British Museum Press, 2001, page 138)
I apologize for my poor interpretation of museum data! Hopefully, soon this piece will be properly identified.