try to look for the wiper relay for replace, but couldn't find it, where is the wiper relay locate at ??
99 civic windshield wiper keep wiping automatic while in driving with switch off on 1999 Honda Civic
Is your Civic a 2-door? Most likely the wiper motor (internal switch failure). Ref. Honda service bulletin #00-031. Without testing anything it's the most likely culprit.