Strictly speaking, the Glimmer Twins are not a songwriting partnership; they're a record producing partnership. Jagger and Richards are indeed a songwriting partnership, but The Glimmer Twins is the joint pseudonym that they use for their record producing credits, mainly with the Rolling Stones but also with other artists.
According to Wikipedia, the name arose in December 1968 and January 1969 when Jagger and Richards were on a cruise with their respective girlfriends, Marianne Faithfull and Anita Pallenberg. 'An older English couple on the ship kept asking Richards and Jagger who they were. When they refused to reveal their identities, the woman reportedly kept asking, "just give us a glimmer" (as in "give us a hint about who you are"), which amused Jagger and Richards.'
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