By strict RAW, yes, provided it didn't lose its magic.
The Dungeon Master's Guide lists rules for downtime activities to create and sell magic items. The price, whether an actual sum of gp for a trade or that of a bill of materials for purchase, depends only on the rarity of the item. The actual qualities of the item don't factor into this, only the rarity.
So, if you had an item that somehow preserved its status as a magic item despite lacking its added functionality, it would technically still be worth something to someone.
Most listed magic items in the DMG that are capable of permanently losing their capabilities (ammunition, absorption ioun stones, wind fan, etc.) clearly state that they lose their magic and become nonmagical in the process, but I was able to find an exception: the chime of opening, which
can be used ten times. After the tenth time, it cracks and becomes useless.
Useless, but not nonmagical. This could be read as a precedent for the possibility of items that are magical but useless, whether built that way like your rock of gravity detection or burned out.
As an aside, if an item is magical and gives some kind of feedback (visual, haptic, etc.) on its status as magical, it can always be used as an antimagic field detector.
By RAI and the surrounding fluff, it's up to the DM.
The DM is given great latitude in determining the availability of magic items, and the DMG explains that a 'magic item economy' (even in the context of D&D's pseudo-economy) doesn't really exist:
Unless [the DM decides that the] campaign works otherwise, most magic items are so rare that they aren't available for purchase... Selling items is difficult in most D&D worlds primarily because of the challenge of finding a buyer.
And even by the aforementioned strict RAW, an item's sale value can vary from 10% to 150% of its rarity value.
A DM is well within their rights to rule that a buyer, presented with an item that is magical but otherwise useless, would not consider the item worth buying.
One could counter with the idea that magic items without their capabilities which are nonetheless still magical are a legitimate curiosity, whether from an archaeological standpoint or a researcher seeking to reverse engineer them, and the very idea of a rock of gravity detection presupposes either a truly mad creator, an unwitting charlatan, or even the possibility of a dimension where these properties don't coincide so neatly and thus it's not so useless after all... but at that point, you've got an actual conversation about the feasibility of such things in such settings, rather than a strict reading of the rules.
