L and I/F are the 2 center terminals. Your alternator HAS NO EXTERNAL VOLTAGE SENSING CIRCUIT. The S terminal wire is missing. The P terminal is a stator tap for AC pulse counting. Not used.
Light circuit in harness is seeing enough ground + bat potential somhow to allow the lamp to glow. So harness or dash board printed circuit board has a fault. Most likely a ground loop due to a POS high resistance firewall connection to ground. Stupid GM electro dipped entire chassis for corrosion coating and caused bad grounds. Another alternator would have done zero to change this.
I ran 16 AWG ground wires from PC board to new firewall ground screw with steel shined bright area. Gas and temp gauges became more accurate. Solid black 22 gauge wires from PC board are OEM ground wires.
Stupid stupid motorhome manufacturer. You can buy a good quality 4-wire reg plug with pigtails. Wire it just like your original plug.
The S wire gets connected to your engine battery + NO SWITCH. This will add .3 volt and auto switch the 1116411 regulator off the internal sensing circuit. This is a simple, piece of cake FOOL PROOF modification that will make your rig like the other 98% of motorhomes on the road.
Plugs are sold in auto parts stores. They are universally superb quality.
Wire that S terminal as close to actual battery post + as you can get it.
Start the engine and put that CS130D to work for a change. It's been strumming its pud charging your batteries.