Found the faucet on the Trekwood site. Their photo shows the faucet to be made by Empire.
https://www.trekwood.com/products/12...Brushed-Nickel
From there, I found this faucet on Amazon, and I found other sites showing the price for one of these faucets to be anywhere from $25 to almost $40. None of the sites show any repair parts for these faucets, and some even say these have a lifetime warranty to the original owner, for whatever that is worth.
https://www.amazon.com/Empire-Faucet...PT4YJR6A1WRQWC
I would suggest just replacing this faucet with a new one, with maybe better quality. If you have removed the screws from the plastic box that the faucet is mounted to, I would also suggest replacing them with stainless steel screws when you reinstall the box, because the screws that are painted white will eventually rust. The faucet may actually be made by American Brass, probably in China, and is just rebranded as Empire.
https://www.rvupgradestore.com/Ameri...-p/71-5703.htm