A BMI search by me revealed that Bob Hamilton was, indeed the original writer, rather than Al Hamilton (who first sang it on a released record), and, it seems that Detroiter, Tom King was added later. It could be that King originally helped Hamilton with the writing and was angered by his being left off the credits and was added later, or that Bob Hamilton needed money later, and sold half his writer interest in that song to King for cash.
Tom King was a well-known Detroit R&B/Soul songwriter from the late '50s into the early '70s. Like almost all other prolific musicians, songwriters, arrangers and producers working out of Detroit during that period, he also worked at Motown for awhile, as did both Bob and Al Hamilton. Not sure if Eugene Hamilton (Ronnie Savoy ever worked for Motown. I've never seen any evidence that he did. The latter may have been working exclusively in New York during Motown's heyday, other than the year or so he worked with Wingate's labels.
I wonder if Tom King was any relation to Maurice King, who was a well-respected piano player, band leader and arranger in Detroit throughout the 1950s, and who was instrumental in developing Motown into the dominant independent Soul music label in the '60s, as piano player and director of Motown's artist development school.