Cogender
Cogender (also spelled "co-gender", with adjectival form "co-gendered") is a term customarily applied by anthropologists to South American Indian (also, Indonesian and other) shamanism in the same sense that the term two-spirit is applied (by North American Indians themselves) to North American Indian shamanism -- in both cases it refers to usually crossdressing (and sometimes homosexual) persons who achieve and maintain shamanic relations with a deity (spirit, spirit guide) through such extraordinary behavior, that particular deity (spirit, spirit-guide) being attracted, fascinated, or even "seduced" by such conspicuously strange, extraordinary display.
Araucan
In Chile, among the Mapuche in La Araucanía, in addition to heterosexual female "machi" shamanesses, there are homosexual male "machi weye" shamans, who wear female clothing. These machi weye were first described in Spanish in a chronicle of 1673 A.D. Among the Mapuche, "the spirits are interested in machi's gendered discourses and performances, not in the [...] under the machi's clothes." In attracting the filew (possessing-spirit), "Both male and female machi become spiritual brides who seduce and call their filew -- at once husband and master -- to possess their heads ... . ... The ritual transvestism of male machi ... draws attention to the relational gender categories of spirit husband and machi wife as a couple (kurewen)." (In ISKON -- the International Society for Kṛṣṇa Consciousness -- male premin-devotees are likewise regarded as quasi-female "wives" of the god Kṛṣṇa.) As concerning "co-gendered identities" of "machi as co-gender specialists", it has been speculated that "female berdaches" may have formerly existed among the Mapuche.
Indonesia
Among the Saʔadan (eastern Toraja) in the island of Sulawesi (Celebes), Indonesia, there are homosexual male toburake tambolang shamans; although among their neighbors the Mamasa (western Toraja) there are instead only heterosexual female toburake shamanesses. Among the Iban of Sarawak (in the island of Borneo, Indonesia), there are homosexual male shamans.