Take inspiration from the anglerfish:
Some anglerfish, like those of the Ceratiidae, or sea devils, employ an unusual mating method. Because individuals are locally rare, encounters are also very rare. Therefore, finding a mate is problematic. When scientists first started capturing ceratioid anglerfish, they noticed that all of the specimens were female. These individuals were a few centimetres in size and almost all of them had what appeared to be parasites attached to them. It turned out that these "parasites" were highly reduced male ceratioids.
Your symbiotic species began as a parasite, probably one that fed on blood from a variety of much larger species. Over time it and your designated host species' ancestor became codependent: the parasite's natural abilities to filter blood benefitted the host, and the successful proliferation of the host benefitted the parasite.
The parasite eventually evolved to burrow under the skin and lay its eggs within the host directly (hosts could support multiple parasites, and parasites are relatively short-lived so this secured a food source for multiple generations). Being attached to the host made mating difficult, but they evolved to rely on contact between hosts spreading their sperm or spores or whatever through sweat.
As eons passed the parasite, now a symbiote, became flatter and flatter under the skin of the host, as to be less intrusive, and harder to dislodge. The coloured patches seen on hosts mark the location of their subdermal symbiotes; the colouration corresponds to minor genetic variations (think racial skin colours). Here they have co-opted the dermis to serve as their reproductive organ, injecting pheromones and sperm into the sweat glands, and using pores to receive the pheromones and sperm of other symbiotes.