After some research I decided this was Launch Complex 21 that was used for horizontal launches of cruise missiles between 1958 and 1963. It initially consisted of a single launch rail, from which XSM-73 Bull Goose missiles were tested. However, between 1959 and 1960, the complex was rebuilt for the MGM-13 Mace, with a second rail added, and a large concrete structure erected around the launch rails.
Below is a picture from the USAF Museum Archives of a MGM-13 Mace missile being launched from LC21.
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