How does a rocking arm voltage regulator work?
Pete Becker found a good description on this forum, to wit:

Inside the voltage regulator you'll find an array of carbon segments arranged in a semi-circle. A pivoting arm rocks back and forth across the carbon segments (hence the name &quot;rocking contact&quot;).
A spring tends to set the adjustment arm in a position for minimum resistance (= more field current = more output voltage.) The tension of this spring is counteracted by an electromagnet that moves the adjustment arm in a manner to raise resistance in response to the generator voltage. Sort of like a giant rheostat, but the arm compresses the carbon segments instead of just sweeping across them.
In other words, No/low voltage - spring pushes the arm for minimum resistance. High voltage - electromagnet (connected to generator output) counteracts spring for more resistance. Correct voltage - spring and electromagnet tension are equal, arm stays where it is. A dashpot or some other form of 'shock absorber' is usually used to damp the movement of the arm.
— B.Sparks

Response speed is going to be controlled by the mechanical inertia of the parts, combined with the action of the dashpot (if any).
Replacing this with an electronic circuit should be straightforward. You need a transistor that can handle the field current and voltage, and a comparator that monitors the output voltage relative to a setpoint to drive it. Be conservative with gain and bandwidth — stability is the key here. You don't want this going into oscillation or even exhibiting any significant overshoot.