Diodes needed (parts) for OR gate automotive relay circuit
The problem you face is the dome light is usually switched on the ground side, via the door contacts. The engine-on is switched on the battery plus side in contrary. You cannot simply diode-or this circuit because you don't have a common potential.

You need a helper relay to overcome that problem. The diode must be rated for the coil current of the power relay. A 1N4001 should be sufficient.







simulate this circuit &ndash; Schematic created using CircuitLab