Gay could have a couple meanings in this case, but only one meaning literally applies to the comparison "as dad's old hatband". See definitions #1, #4, and #5 on dictionary.com and search Google Images for hatbands for reference.
1. of, pertaining to, or exhibiting sexual desire or behavior directed toward a person or persons of one's own sex; homosexual: a gay couple.
4. Older Use. bright or showy: gay colors; gay ornaments. Synonyms: colorful, brilliant, vivid, intense, lustrous; glittering, theatrical, flamboyant. Antonyms: dull, drab, somber, lackluster; conservative
5. Older Use. having or showing a merry, lively mood:
gay spirits; gay music.
King may be informing you that Nelson is gay in the sexual sense, but the comparison "gay as dad's old hatband" is using the term in the brightly colored or jolly sense.
Since the usage of "gay" to mean "exuberant" could be obvious in the context of describing the character, the part about him being non-heterosexual would be a double entendre.
King could be getting at a few things here:
1) that although Nelson does not outwardly portray it, he is a flamboyant [brightly colored, like the hatband dad wore] homosexual at heart.
2) he could be using the other two meanings in conjunction to describe that Nelson is passionately joyful and loving, despite his gruff outward appearance.
Or, 3) some combination thereof (the ambiguity seems to be purposeful on King's part).
Reference: King uses the phrase "gay as old Dad's hatband" to describe an LGBTQ character.