A sundowner was something that Major Daly offered both his daughter and her "young man" while onboard the miniscope-trapped SS Bernice. Both refused, preferring instead to take a walk on deck. The major, meanwhile, poured himself a drink from a single decanter containing a whiskey-coloured liquid into a highball glass, and then tried to finish his book. (TV: Carnival of Monsters)
Behind the scenes
In the real world, a "sundowner" is just a drink imbibed at sundown. It's not any specific drink, but merely British slang. The episode supports this by clearly showing how the major prepares his drink.