Is there any proof that the Berdache or a "third sex" assisted in
matchmaking (the pairing of straight males and females) in their
culture?

Hi Simoetry,

I did find this:

"Because of their unique position as neither male, nor female,
berdache would act as counselors for marital conflict. Among the Omaha
tribe, they were even paid for this service. Berdache also performed
the role of matchmaker. When a young man wanted to send gifts and get
the attention of a young woman, the berdache would often act as ago
between with the girl?s family (70-71)."
The citations are not standard but I think the reference is from
Williams, Walter L. The Spirit and the Flesh, Sexual Diversity in the
American Indian Culture. Boston, Beacon Press, 1986.
http://members.tripod.com/~Berdache_Two/twospirit.htm

There are many records of 'third-sexes' as religious leaders, wizards,
shamans and oracles which in many societies would involve such tasks,
but without specific mention.

I will let you know if I can find anything further.