Oh, Sayge is easy to find. That shop is basically one giant room. The closest there is to a separate space is that the tubs for dyeing are tucked in under a cover platform for safety.
(No, Nintendo, there are not trap doors on those platforms to dump a customer into a giant vat of dye. That is not how dyeing really works. As amusing as a customer's face would be when they realize they're about to be dunked, that is a good way to poison your customer, and ruin those poor clothes.)
Sayge was back at his work station where he worked on perfecting formulas for dyes before taking the clothes up to the platform to pre-treat them however they need to be before getting tossed into the tubs. He heard Link's somewhat familiar voice behind him and glanced back in time to see the young (old?) man zip off and leave the queen giving him a dirty look at his back before coming into the store.
He turned slightly, still slowly stirring a new formula for indigo dye in a test tube as he greeted her. "If my eyes don't deceive me, the queen is a customer. Welcome to the Kochi Dye Shop, where we live to dye. Hue do you do?"