Did you ever get to the bottom of this?
It sounds like a short circuit on one of the large supply wires, either to the alternator or to the starter (I think that is where it goes). As I recall, there is a poorly-done factory splice below and slightly behind the fuse block beside the driver's shock tower.
I personally recommend a battery relocation, you won't believe how much better my '86 has worked ever since I relocated the battery (nothing original - behind the passenger's seat).
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1986 GXL ('87 4-port NA - Haltech E8, LS2 Coils. Defined Autoworks Headers, Dual 2.5" Exhaust (Dual Superflow, dBX mufflers)
1991 Coupe (KYB AGX Shocks, Eibach lowering springs, RB exhaust, Stock and Automatic)
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