Originally Posted by Martin_R
Electronic relay should still fix the issue. Normal relay needs resistance in order to fire. Electronic relay blinks away no matter what the resistance on the wires is.
Slight correction: standard relay does not require resistance to flash normally, it requires current through bulb to be high enough to indicate good bulb. Because LEDs have very low current requirement, it senses this and flashes fast to signal burned bulb. To remedy this you need to add another electric path to increase current through relay - low value resistor parallel to LED bulb, so more current flows through it then through lamp itself.
These halogen bulbs also are rated for only 0.5A (standard bulb is more like 2A), so need parallel resistor to draw more current and fool relay. You can use electronic flasher like for LEDs - it blinks at constant rate regardless of current flowing through it.