Maybe the alternator wire to the battery or the starter to battery wire is internally corroding and needs to be replaced. Could be bad battery clamps, or bad connections at the auxilary ring terminals at the battery positive clamp, which supply juice to pretty much everything on the car. IIRC I got around 13.8v with a brand "new" rebuilt alternator and it still did dip a little under load (mostly the radiator cooling fans). The idle does get a little rough when the cooling fans come on, and a new battery didn't do anything for that, so I may need to look into a wiring upgrade. (hmmm...another epic project materializing as we speak
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