Engine stops when I pull the battery cable off?

That's a good thing. Removing a battery cable is a real good way to destroy multiple computers on any vehicle and any bulbs that are turned on. That "test" doesn't prove anything as far as system operation is concerned. When doing so, an engine with a defective generator can continue to run, and one with a perfectly fine generator could stall. All AC generators put out three-phase output which is very efficient, but it does have small voltage pulses called "ripple" voltage. The battery is the only component that smooths out that ripple. Without the battery in the circuit, the high spots in the ripple voltage go right back to run the field circuit inside the generator. That higher voltage creates a bigger magnetic field which leads to higher output voltage. That cycle repeats over and over until output voltage could go over 30 volts. What can save you is all generators are relatively inefficient at lower speeds. That's why when performing a professional load test, the testers always require us to raise engine speed to 2,000 rpm.

Some voltage regulators, including Ford's newer version in the mid '90s, monitor system voltage for an over-charge condition as well as an under-charge and no-charge condition. Those will respond to excessive ripple voltage by cutting back on generator output, often to the point the engine stalls.

The proper way to test the charging system is with an inexpensive digital voltmeter. This article explains it in more detail:

https://www.2carpros.com/articles/how-to-check-a-car-alternator

They're using an "auto-ranging" voltmeter here. That's an expensive feature you don't need. If you need help setting up your meter, I can help with that.

Start by measuring the battery's voltage with the engine not running. It should be 12.6 volts if it's good and fully charged. If it's closer to 12.2 volts, it is good but discharged. Charge it at a slow rate for about two hours with a small portable charger. If the voltage is 11.0 volts or less, it has a shorted cell and must be replaced.

Next, measure the battery voltage again with the engine running. Now you should find between 13.75 and 14.75 volts. If you do, the system is working, but that only means it is okay to perform the rest of the tests. Those require a professional load tester. It will measure full-load output current, regulating voltage, and ripple voltage. Most testers just show ripple voltage on a bar chart display, but those that can make printouts of the results will list a voltage for ripple voltage. Normally we're just looking for "low" or "high", meaning normal or excessive.

If ripple voltage is high, it is due to one failed diode of the six inside the generator. With one bad diode, maximum output current that can be developed will be exactly one third of the generator's maximum rating. 30 amps from a common 90-amp generator may not be enough to meet the demands of the electrical system under all conditions. The battery has to make up the difference as it slowly runs down over days or weeks. Two head light bulbs can draw a total of ten amps. There's also the running lights, fuel pump motor, and ignition system that can draw another ten to 15 amps.

You didn't say what kind of problem you're trying to solve so I can't address that. If I need to look up the charging system diagram, you'll need to list the engine size and van size so I post the right parts photos and diagrams. Depending on the type of problem, you may also find valuable clues by observing the operation of the "Battey" light on the dash. It must turn on when you turn the ignition switch to "run", then turn off when the engine is running.

This drawing shows ripple voltage. The top waveform is typical for a properly working system. Professional load testers will show it as "normal". If it's measured for a printout, it will be listed as 0.5 volts, which is pretty low. The lower waveform shows what happens when one diode has failed. One of the three phases is missing. During the time that output isn't there, the output voltage drops real low, in this case, to 9.3 volts.