This was previously misidentified by me as a dung fly, Scathophagidae, I now realize (thanks to Keith Bayless) is a Heleomyzid, Suillia. This fly, was exhibiting peculiar behavior--one fly was very attached to one stinkhorn mushroom, Phallus ravenelii. As I moved in to photograph it, if it shied away, it would return and perch on the top or edge of the cap, often holding one wing out in an obvious display. Doing "a Google" (as some say), I found that this territorial behavior has been seen in the genus in Japan, so I am presuming this is a male:
Tuno et al., Territorial behaviour of Suillia males on basidiocarps of Hebeloma radicosum in central Japan. Mycologist (2003), 17 : 122-125 abstract, quoting:

Usually one Suillia fly (male) occupied one basidiocarp and prevented other conspecifics from occupying the same basidiocarp. This appeared to be pre-mating territorial behaviour. Larval stages of Suillia are known to be mycophagous, and the territorial behaviour is presumably performed to defend oviposition sites.