The buffy spectacle and lack of rust in the tail help to rule out the similar Hermit Thrush, a much more common resident of the Chiricahua Mountains.
Swainson's Thrush in Portal AZ (Photos by Narca)
Over the past 15 years while working in the bootheel of New Mexico, Alan and I have only encountered Swainson's Thrushes on four occasions, twice while banding at Clanton Cienaga. They seem to move through the region during a narrow window of time, from about May 11 through about May 31. That's now, so ¡ojo! –– keep your eyes open!