Ermmm… If you use several pins to get the current rating, what happens if one of the pins fails or gets corroded? Won’t you risk generating heat? Think I’d prefer nice big connectors for the power and to keep the data lines safely segregated. Depends on your needs and design I suppose.
Not sure I understand the problem fully, but you want a circuit to operate when you push the horn button, without affecting the horn operation.
Chances are the relay coil is drawing to much power.
Have you thought about adding a transistor to your circuit? It would draw very little current from the horn circuit but should allow you to drive something else. - such as your relay. It would of course require you to do some electronics.