Alan Slatin, 58, general manager of a private country club from Lincolnshire, Ill., on his family’s one-of-a-kind handmade pickup, as told to A.J. Baime.

My grandfather, Andrew Slatinsky, worked in mechanical trades. When he retired in the late 1960s, he decided to create a hand-built vehicle that would be unlike anything else on the road, out of his home in Mattawan, Mich.

The...