The Nite Owls had this one 45 on the Top Dog label of Louisville, Kentucky. Both songs sound very different from each other. “Act Your Age” is a good put-down song, written by Robby Burnfin and published by Fall City Music of Louisville.
“Act Your Age” sounds up-to-date for 1966. The flip is definitely from an earlier era, a cover of “Nite Owl”, written by Bernice Williams and originally done by the Dukays (who would later hit with “Duke of Earl” with Gene Chandler on vocals). Featuring a horn section instead of swirling organ, it could have been recorded at an earlier session.
I don’t think there’s any connection to the Illinois-based Nite-Owls who released “Come On Back” / “It’s a Hassle” on Rembrandt. I really don’t have any info on the band or their members.