Mmm. When you replace the factory wiring with an aftermarket harness, you take all the understanding and debugging on yourself. Do you have a wiring diagram for the new harness? That the alternator is from an S10 (?) is kind of irrelevant. Or maybe you mean 10SI? That's a type of Delco alternator. These need 3 wires - the exciter from the ignition switch, the large charge wire to the battery, and the voltage sense wire that typically wraps back to the charge wire. If you have this type of alternator, I suggest you learn how these connections work and see how they are wired in your harness diagram.
Maine beekeeper's truck: '77 J10 LWB, 258/T15/D20/3.54 bone stock, low options (delete radio), PS, hubcaps.
Browless and proud: '82 J20 360/T18/NP208/3.73, Destination ATs, 7600 GVWR
Copper Polly: '75 CJ-6, 304/T15, PS, BFG KM2s, soft top
GTI without the badges: '95 VW Golf Sport 2000cc 2D
ECO Green: '15 FCA Jeep Cherokee KL Trailhawk