I'll probably write another article on the star tracker itself. But I can give you a quick summary of the spiral search mechanism. It was electromechanical: a motor turned a resolver, a device with coils to generate sine and cosine from the shaft angle. This gives the X and Y deflections for a circle. These signals went through potentiometers that were also turned by the motor to produce constantly growing magnitudes, so you get a spiral. But you need to slow down the motor as you spiral outwards since you're covering a much larger linear region. So the motor also turns a stepping switch that progressively reduces its speed.

Once the system finds a star, a complicated feedback mechanism keeps it locked onto the star. There is a spinning slotted disk in front of the photomultiplier tube. If the star is off center, the output will peak when the slot lines up with the star. Thus there is an error signal with phase that indicates the direction to the star. This signal is demodulated to produce X and Y signals that change the aim to move towards the star.