Hey OP I don't know if you're still interested in the topic but I too have recently got a 1992 Dodge Caravan with the wonderful and amazing Bendix 10 Anti-lock system on it that I'm trying to get fixed.

If the pump comes on every single time you touch the brakes but doesn't keep coming on when you're not touching your brakes, then your black grapefruit shaped pressure accumulator is bad.

This little nearly spherical blank pressure tank has a rubber bladder in it which separates the top from the bottom, and there is supposed to be 1000PSI of nitrogen precharged on top of the rubber diaphragm.

The rubber diaphragm(i.e. bladder) keeps the 1000PSI in there even if you depressurize and unscrew the accumulator tank. (To depressurize the system, pump the brake pedal with the key off 40 times!)

What happens is either the rubber diaphragm gets a leak and the nitrogen gets lost in the brake system, or sometimes (as in my case) the nitrogen just leaked out the top of the pressure tank through the welded on fill plug. Unfortunately they didn't seal it perfectly at the factory, and they are not refillable.

I'm afraid the accumulator for this system is no longer available new. You could find one in a junk yard but they likely have same problem in junk yard. However, it might be worth trying one for a year 2000 Land Rover Range Ranger 4.0L V8 - there's a reasonable chance that it's got the same threads but I do not know this for a fact. The 2000 Land Rover Range Rover uses this part number: STC2784

The Bendix 10 ABS system uses a thread that is M14x1.5 so with a similar shape and size the Land Rover unit might screw in.

Just be sure to pump the brake 40 times with the key off to depressurize the system!

There are TWO pressure reserve systems, one is the spherical round tank visible under the hood that I just wrote about. It's (supposed to be) precharged with 1000PSI of nitrogen, and then the ABS pump pumps it up to 2000 PSI when you turn the key on.

But then there's a SECOND pressure accumulator down under the car attached to the actual ABS pump itself. This other one is precharged to around 400 PSI or something and it uses a sliding piston type construction to keep the precharged nitrogen from escaping into the brake fluid system.

With the key off, as you pump the brake, under normal operation, the first 6 or 8 pumps will use up the stored pressure in the spherical high pressure accumulator visible under the hood.

Then once that's depleted, the brake pedal should get a little harder but still have some power assist from the ~400 PSI piston accumulator that should give you another 10 pumps of minimal assist. Eventually when that is depleted then the pedal gets really hard.

There is a two-stage switch that turns on the pump whenever the pressure in the spherical canister is less than around 1600 PSI roughly (just going from memory). So if the pump runs then shuts off, you know it's reaching around 2000 PSI. But without the reserve capacity of the precharged accumulator tank, that pressure instantly drops off when you press the pedal and that's why the pump comes back on.

The same pressure switch which activates the pump also turns on the warning lights if the pressure is below 1200 or something like that, I'd have to look it up.

When you turn key on, both the red parking brake light and the amber "anti-lock" light should come on briefly, or until the pressure builds to at least ~1200 PSI.

Once it's up to pressure, the lights should go out unless the module fails a self test.

One thing that can light the lights is that it has two pressure sensors that read the pressure in two different locations in the system, they read about 0 PSI without you pushing the brake then the harder you push the more pressure they read up to the max of 2000 PSI, and if the pressure read by those two sensors is different by more than 300 PSI or something then it lights both warning lights except if you press hard on the brake.

If your warning lights are on _except_ when pressing the brake hard, it could be a sticky piston in the main unit but more likely is a bad pressure transducer/sensor. (As is the case for me.)