How phenotypic diversity originates and persists within populations are classic puzzles in evolutionary biology. While polymorphisms hypothesized to be under balancing selection segregate within many species, it remains rare for the genetic basis and the selective forces to both be known for the same trait, leading to an incomplete understanding of many classes of polymorphisms. Here, we uncover the genetic architecture of a balanced sexual mimicry polymorphism and identify behavioral mechanisms that may be involved in its maintenance in the swordtail fish Xiphophorus birchmanni. We find that ~40% of X. birchmanni males develop a "false gravid spot", a melanic pigmentation pattern that mimics the "pregnancy spot" associated with sexual maturity in female live-bearing fish. Using genome-wide association mapping, we detect a single intergenic region associated with variation in the false gravid spot, which is upstream of kitlga, a gene involved in melanophore patterning. By performing long-read sequencing within and across populations, we identify complex structural rearrangements between alternate alleles at this locus. The false gravid spot haplotype drives increased allele-specific expression of kitlga, which provides a mechanistic explanation for the increased melanophore abundance that causes the spot. By studying social interactions in the laboratory and in nature, we find that males with the false gravid spot experience less aggression; however, they also receive increased attention from other males and are disdained by females. These behavioral interactions may play a role in maintaining this phenotypic polymorphism in natural populations. We speculate that structural variants affecting gene regulation may be an underappreciated driver of balanced polymorphisms across diverse species.