I have no memory of her, apparently Rodeo Rose - https://muppet.fandom.com/wiki/Rodeo_Rosie
In looking her up...
Thought it might have been ^ the prototype of this "cowboy" also featured in the later years cast pic
Have a vague memory of him as he was a recurring character, Ironically his name is "Forgetful Jones" LOL!
Besides the Muppet wiki- https://muppet.fandom.com/wiki/Forgetful_Jones
Looking him up came across this wonderful series of vids- 50 Retired Sesame Street Muppets, this is (Part 2):
Jump or click- 13:17 for Forgetful Jones.
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He's also upfront between Oscar and Ernie here. Love this ^ cast pic!.