Here's a circuit that should do what you want.
Here's a circuit description.
The circuit connects to an automotive power supply of +12V (nominal) and 0V using CN1 and CN3. When this voltage is higher than a set level, for example 13.0V, relay K1 is activated, and feeds the +12V supply out on CN2. The relays specified are rated for 2A switching and carry current; if more current is needed, an extra interposing relay should be used.
U1 (TL431AC) is a shunt voltage regulator that is used here as a voltage comparator with a fixed detection voltage of 2.5V. When the ADJ pin goes over 2.5V, U1 will conduct current through its K and A pins, activating the relay. D1 protects U1 against back EMF from the collapsing magnetic field when the relay is turned OFF.
An adjustable fraction of the battery voltage (which comes from CN1) is provided into U1's ADJ input. This voltage is smoothed by C1 to prevent U1 from responding to noise and rapid variations. Hysteresis is provided by R2 and R3, and provides a voltage deadband between switching ON and switching OFF; this prevents chatter and indecision when the voltage is near the threshold voltage.
Initially assume that K1 is open and the voltage at the top end of R3 is negligible. If VR1 has been adjusted for a 13.0V voltage threshold, VR1's resistance can be calculated as 2.5 / ((13.0 - 2.5) / R1) which is about 6430 ohms.
Once the supply voltage reaches this threshold and the relay turns ON, current through R2 raises the voltage on R3 to about (13 R3 / R2) which is about 48 mV. The supply voltage required for the voltage divider to yield 2.5V on U1's ADJ pin has now dropped to (((2.5 - 0.048) / VR1) * R1) + 2.5 which is (2.452 / 6430 * 27000) + 2.5 which is about 12.8V. So a hysteresis deadband of about 0.2V is created.
R4 protects the circuit against surges at load dump; only minimal protection is needed as there are no ICs connected across the supply rails.
The relay types given are all high-sensitivity relays; coil current is 12.5 mA or less. The IMB06 parts are TE Connectivity brand; the G5V is an Omron part. They are all rated for a maximum switching and carrying current of 2A; if more is needed, an external relay must be used.