The oldest records for the address (1955) comes up with the home of Sunset Trailer Court which occupied the block. In 1962 Beltone Hearing Testing Laboratory opened under H.R. "Tex" Mayhall though within a few years Mayhall relocated to Austin. (It likely used Sunset's office.) By the mid 1960s the address was home to Wilie Trailer Sales, with Denny's opening a new restaurant on the site in 1969.
After a run of ten years, the Denny's changed hands. Under new owner J. Carlos Hongo, the name changed to Carlson's, which dropped 24 hour service while adding items like Kobe Teriyaki Steak to the menu. However, Carlson's closed in early 1982 and soon reopened as Kettle, which featured 24 hour service once more, and that 24 hour service would continue for almost forty years (ending in 2020).
The demise of the College Station location meant that this is the only Kettle remaining in the area. Besides the Arizona one, that Laredo location I'm not 100% sure is open anymore. It looks rather desolate these days.