I'm stumped with this problem, and even the dealership has no idea why or how it's happening.
2006 Civic 1.8 lx 5speed

I can set cruise, speed up and down just fine. But as soon as I turn on the headlights, the cruise will disengage, and I won't be able to set it. The cruise module light and switch works fine, but you can't set a speed.

Ive tested both the brake and clutch pedal switch, and they work fine. I also checked all of the accessable grounds related to the cruise control module, and those were tight.

I heard that led bulbs can mess with the system, so I tested out my old incandescent bulbs all around. Still no difference.
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Probably due to a short in the wiring that goes to the under-dash fuse box; or at the MICU, which is part of the under-dash fuse box.

Both headlights and cruise control circuits' wires goes through an under-dash junction box, under-dash fuse box, and MICU. Short may be anywhere along those circuit wiring and/or components.