He and Happy New Year seem to at least be partially inspired by their counterparts from the 1978 Rankin/Bass film, Rudolph's Shiny New Year.
When Billy, Mandy, Irwin, and Grim visited the Halls of Time on an alternate field trip, Father Time introduced himself and Happy New Year and served as their tour guide. When his back was turned, Billy and Irwin ran off to find some amusement. Mandy soon followed to discover what trouble they were up to. By the time Father Time noticed they were gone, Billy and Irwin had already found their way to the hourglasses and caused considerable damage. Father Time forced the boys to put back all of the stolen hourglasses, including their own as well as those of Grim and Mandy. Father Time then demanded Billy, Irwin, Many, and Grim to leave after informing Billy, Irwin, Mandy and Grim that they that have broken the rules. However, Billy and Mandy put their hourglasses wrong side up, and the three children and Grim began to quickly regress in age. Father Time refused them reentry despite this fact. Grim wrested Father Time's scythe away from his grip and used it to fly him and the children back to the hourglasses. However, Irwin, Billy, Mandy, and Grim all age regressed to nothingness before any of their hourglasses could be turned right side up.
Father Time shows enthusiasm for his job, calling the Sands of Time "pretty slick", though he is also willing to admit which parts of the Halls- the gears- are "merely for show". On the other hand, he may not be the most attentive of visitors, as he failed to notice Billy, Irwin, and Mandy when they sneak off. On the other hand, once he notices transgressions, he demonstrated a quick change to a cranky disposition that he suffered no fools. He even stood by his decision to banish the unruly visitors even if it meant their dooms.