No way you can diagnose this without a VOM. One for about $20 from Sears or Radio SHack will do fine. You want to check the voltage at the back of the alternator and at the battery.
Then you can use it to find an open ground or open wire from the alternator to the battery etc. Big wire probably from batery to starter then from starter to alternator? Glowing bulb may indicate a short somewhere, maybe a wire or the alternator.
Sounds like you have the external mechanical regulator.
If you HAVE to replace the alternator I'd change to one with the internal regulator.
It may be you just have some bad wiring though, or a bad mechanical VR.
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744 & 745 GLE's (IPD a-sbars)16v M46, 245 SE(IPD a-sbars) auto, 242Ti M46(IPD springs and bars), 745GL 8v auto