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Rather simple. The analog TV system worked, by scanning the image line after line. The movement of scanning beam was controlled by very precise electronic timer (the time base). During each scan period, each pixel of the image was scanned at precise time, determined by time base. So the position of each pixel could be easily determined by the time base signal.

The "Walleye" seeker was a contrast seeker - which means that it tracked the high-contrast spots that stand out on the background. For example, a dark window on the white building wall. When the scanning beam moved over such contrast spot, there was a sharp jump in the voltage. The small logic circuit reacted on such jump, and stored the corresponding time base signal voltage in its capacitor. So: the circuit "memorized" where the scanning beam was at the moment the signal jumped. I.e. circuit memorized, where in the camera field of view was a contrast spot.

The seeker moved camera in such way, that the contrast spot stay directly in the center of image. The camera was set on the gimball, so it could move independently of the bomb's body. The bomb autopilot them tried to align the longitudal axis of the bomb body with the axis of the camera.

I made this little gif a few years ago to demonstrate, how TV contrast seeker of "Walleye" caught the moment when the output signal jumped.