Wouldn't the object need to be something of deep importance to the individual or be a poetic representation? I always assumed the volleyball was a symbol of everything he left behind. Things like recreation no longer mattered; only survival. :shrug: but I also thought the movie sounded incredibly boring. If you want a random item, go for qualities like "awkward to carry" or "gets hot when left in the sun". Give your characters personality or force them to choose that object at a moment it's inconvenient.

• An oversized diamond/ faberge egg - it's valuable, heavy or fragile and inconvenient, in a critical moment your character may need to smash it against something risking damage
• Teddy Roxbury/furby - favorite toy growing up? Creepy voice at stalking moments? Mid point twist when the batteries die?
• Harmonica - potentially a little Disney princess forest friend vibes
• Bowling ball - Wilson prolly plays a little different when it's not feasible to take him on a raft, prevents you from climbing trees and burns precious calories transporting. Mobility is now a plot point. Decent weapon tho
• Toilet plunger/brush - everyday object that can be utilized differently, maybe adds that little bit extra reach to save the day?