1998 honda civic both headlights remains dim on low beam and high beam?

it could be a bad wire

if the hi beam signal is on with the low or hi then the wires must be touching it happened to me before

also you may wanna check all the wires under the hood and maybe check the alternator just to bee sure

Most likely the bulb. Your Honda uses a commonly available HB9004 headlight bulb, which has separate filaments for low beam and high beam. It's common for the low beam filament to burn out first, because it's used more often than the high beams. They're pretty inexpensive -- ten bucks or so ought to buy you a new one. As a recommendation, buy two and do the passenger's side as well, because it's probably within a few hours of burning out too.

your going to have to replace the damaged wires could be as simple as part of the connection got wet and fried

have the alternator and battery checked. the alternator brushes could be worn some and not charging the battery like it should.