2000 Honda Civic EX 4 Cyl 1.6L
Why do my headlight and dash lights flicker while drivng?
Obviously there is a loose connection that they both share. You would need to find the power (hot) wire for your dash lights and follow that to the place where your headlight wiring intersect. That's likely where your issue is. Also, check the fuse or just replace it to be sure.