I have a second hand 2003 Civic and as the title says, the brakes have about 2-3 inches of travel before working normally. I’ve bled the breaks which has made it less spongy but the travel is still there. The brake pads although aren’t new, do have lots of life left in them. I’ve opened the place where the rod connects to the brake booster and it’s perfect. No gap in the hinges. I can’t find anything online that describes the problem. My final guess is it’s either the brake booster itself or the caliper(?).

PS brake lights come on at the top of motion. Not sure if that’s any help