The second published illustration of Gollum to see the light of day came in the "J.R.R. Tolkien Calendar 1975", printed by Ballantine Books. Although Allen & Unwin (Tolkien's British publishers) had issued calendars before, they all contained art by J.R.R. Tolkien. And Tolkien never drew Gollum.
The artist was Tim Kirk. While in high school in 1964, Kirk read Tolkien and was enthralled. A lifelong artist, Kirk received his BFA (emphasis in commercial art) in 1971 and his MFA (illustration) in 1973, both from Cal State-Long Beach. Was the MFA a foregone conclusion? Perhaps. Kirk won the Hugo Award for Best Fan Artist in 1970, 1972, and 1973, and would go on to win it again in 1974 and 1976. He and Ken Keller co-designed in 1976 the resin die use for the Hugo Award.
Kirk had spent years drawing characters and scene from The Lord of the Rings and The Hobbit. In 1972, he exhibited 26 paintings based on The Lord of the Rings at Worldcon. Ian and Betty Ballantine, co-founders and publishers of Ballantine Books, purchased the entire collection. In 1975, 13 of these paintings were published as the "J.R.R. Tolkien Calendar 1975".
What's interesting about Kirk's Gollum is how humanoid he is. He lacks the saucer eyes and frog-like appearance which Tolkien described. Instead, he's more like a long-fingered, boney human being (easily double Bilbo's height!) with a sloped forehead and prognathic jaw.