Sadly, all you can do is sell it
During Chapter 6 of the Resident Evil 4 remake, you’ll come across the Chief Mendez boss fight. As one of the more memorable moments of the original, the stakes are just as high this time, as you’ll go through a ton of resources to take him down. After he is down, don’t forget to grab his False Eye!
You’ll get Mendez’s False Eye after the Chief Mendez boss fight
After finishing off Mendez, he’ll collapse to the ground and his False Eye will roll out of his head. Don’t worry about being swift here, as the barn won’t implode or anything. You have time to pick up everything you may have missed from the area: including the false Eye
We have a full boss guide on Mendez here.
Mendez’s False Eye is not a key: you can either hold on to it or sell it
In the original version of Resident Evil 4, Chief Mendez’s False Eye was a “key item” that you needed to use during the course of the game. Now, it’s merely a trinket to sell to The Merchant. Selling it off will net you 12,000 Pesetas.
Note that there is nothing that can be socketed into the False Eye, and there’s no benefit to keeping it around unless you want to.