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I'd echo what wiswind said about checking the alternator connections very carefully, even to the extent of removing, cleaning and reconnecting them, and I would do that for all connections associated with the alternator, rectifier, voltage regulator and battery (the rectifier may be internal to the alternator and hence not accessible). Don't reassemble them in a dry state - smear them with a protective compound first. Here in the UK, I use something called petroleum jelly, trade name Vaseline, available from any pharmacy but if that doesn't sound familiar then use whatever compound you would commonly use over there to protect battery terminals.

I don't know anything about Windstars but my instincts as an electronics engineer would make me suspect a bad connection somewhere amongst those items, or an intermittent short-circuit either in one of the diodes within the rectifier pack, or in one of the semiconductors within the voltage regulator assembly.

The alternator generates an alternating current (AC) which the rectifier pack then converts to direct current (DC), and the voltage regulator is responsible for ensuring that that current is fed to the battery at the correct voltage level. The charge indicator warning lamp on the dashboard will be configured in different ways depending on the particular vehicle, but essentially they all indicate the same thing - when the voltage at the battery exceeds that at the regulator (battery discharging) the lamp will light, and conversely, when the voltage at the regulator exceeds that at the battery (battery now charging) the indicator will extinguish.

In the event of a momentary short-circuit within the rectifier or voltage regulator, the voltage output could drop dramatically and therefore the charge indicator lamp would light. For the duration of the short-circuit, current would flow from the battery through the short-circuit path, and the voltage at the battery could dip dramatically, very briefly, for the duration of the event, and with the complex and sensitive nature of the myriad electronic modules which control today's engines, that brief voltage drop might just be enough to cause a glitch (momentary malfunction) in one of the control modules and stop the engine from running.

That's only hypothesis, but for what it's worth, I'd definitely look first in the direction of the alternator and its associated components and wiring.