Although this is the "first" character to take the name El Papagayo within the time frame of the DC Universe, the other Batman villain pre-dates him as that version appeared first way back in 1949 but was left in obscurity before being revived years later by writer Grant Morrison.
He first appeared in Jonah Hex #2 (1977) created by writer Michael Fleisher and artist Joe Luis Garcia-Lopez.
Major Story Arcs
El Papagayo was a Mexican bandit during the 1800's. Jonah Hex first encountered him when Quentin Turnbull tricked him into infiltrating his gang as Hex believed he was working on behalf of the Secret Service. Hex failed to stop El Papagayo and the two later crossed paths several times becoming bitter enemies.
Jonah Hex is revealed to have eventually killed El Papagayo in the graphic novel Jonah Hex: No way Back.