The Gimlet is a martini with Rose's Lime Juice instead of vermouth. It's that simple. While you might find a few recipes out there that include some simple syrup (and frankly I like it with the sweetener) - that is not a true Gimlet.
The Vodka Gimlet simply replaces the gin with vodka.
I myself prefer fresh lime juice to Rose's - and a key lime is even better but according to the character Terry Lennox in Raymond Chandler's The Long Goodbye:
"a real gimlet is half gin and half Rose's lime juice and nothing else"
He's got a point - changing the Roses to fresh lime gives this cocktail an entirely different flavor as Rose's has it's own unique taste. Still, I prefer fresh juice.
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