What is happening is the relay uses the headlights bulbs as the ground for the relay- factory setup!!!

so if you do the headlight relay upgrade for the bulbs you take away the "ground for the relay to work.

did this several years ago for another car- what I did was replace the orginal relay with a Bosch type-still use the circuit breaker, but use a physical ground wire from the relay to the dash frame to make it work correctly.

diagram attached