I used to have a Stars explorer-shaped bass (now in the hands of another club member) which also had a StarTone preamp. Here's the description I got a few years ago from a fella out in the Bay area who worked at Stars:
The Startone is a state variable sweep filter, similar to the Alembic Bass design but with much simpler circuitry. The rectangular, two section black pot is the sweep. It goes across the spectrum from 40hz up to about 2Khz in an approximately one octave bandwidth. The shorter black rectangular pot is the gain and will give you up to +18db boost or down to -18db cut at the frequency the sweep pot is set at. The switch is a bypass.
The batteries are paralleled so that they still only supply 9 volts to the circuit but last a lot longer than one battery. You can use two or only one. With one battery you should get between 40 to 60 hours continuous use. If you decide to use only one battery, put some plastic foam or piece of a sponge in the compartment to keep the single battery from flopping around. I can't see the output jack, but it should be a rectangular black type. It has a shunt on it that turns the circuit on when a cord is plugged in, and off when you unplug it. So, don't leave the cord plugged in when you are not playing it as the batteries will continue to drain.
Seeing the caramel colored potted circuit I can say that the Startone is a second generation made somewhere between 1980 and 1982. I redesigned the existing circuit board to be about half the size of the first generation making it a lot easier to fit into existing control cavities without additional routing.
From the pics it looks like your setup is a little more elaborate than that on my old bass, but I thought I'd pass the info along anyway.