It’s called a Twilight Sentinel, it’s a sensor that signals the lights to turn on automatically, a much earlier design of what we use today on our new cars , that little bulb looking thing on top of your dashboard close to your windshield.
OK.. A correction on what Ray was saying. There were two headlight control options on 1964 Cadillacs - the Twilight Sentinel which turned lights on at dusk and off at dawn and controlled by a small round photocell on left front part of dash, and the Guidematic Power Headlamp Control (Automatic Dimming) which was controlled by a phototube mounted in left fender behind a clear fender tip extension.
1964 Cadillacs, except Series 75, with factory installed Auto Dimming, had the clear fender tip extension. Dealer installed Automatic dimming (and Series 75) units had mounted Photocells as they had been in 1963.
Twilight Sentinel was a new feature for 1964. Below are factory literature scans for the Guidematic Auto Dimming and Twilight Sentinel, and a picture of the Twilight Sentinel photo cell.