Here is a circuit that has a precise cutin of 13.05V, and a cutout of 12.05V, assuming you use the specified 1% resistors. R7 controls both cutin and cutout. R1 controls the hysteresis.
View attachment 91676
If you feed it from one of the key-switched accessory circuits, it will begin with the relay off, and the relay will not turn on until the alternator comes on line and the battery voltage comes up... With the hysteresis, it shouldn't ever go off, even if waiting at a stop light with the engine idling and the AC running...