There are two kinds of gimlets, apparently, one made with Mother Russia's anesthetic of choice and the other with gin. Since you're an angelic mocktailer, you'll possess neither of those two firewaters in your bar. One thing that you will need, however, is some Rose's Sweetened Lime Juice. If you're going to be throwing mocktail parties, this chartreuse syrup should be an on-hand staple.
A few other things that you might need:
A cocktail shaker
A few different glass shapes
In the picture below is a martini glass (the one with a wide mouth) and a tumbler. A gimlet is usually served in a martini glass with a lime garnish. Also pictured are the three parts of a cocktail shaker. Don't fret, you can find two hundred cocktail shakers on clearance for probably five bucks at your local TJ Maxx. The point of a cocktail shaker is to combine a whole bunch of liquids, ingredients, and often ice, shaking them to combine and then straining with the built-in strainer.
For our simlet you'll need ice, sweetened lime juice, mineral water, and a sprig of fresh rosemary. You don't want a fizzy drink in this case, so no club soda. Put ice into the shaker, add about a cup of water, two-ish tablespoons of sweetened lime juice, and about an inch's worth of rosemary. Why rosemary? Because it gives just a hint of woodsy herb to the drink, kind of a similar feeling as gin (made from juniper berries) might impart. You can leave it out; your house, your rules. Put both tops back on your shaker. SHAKE.
See? The liquid is cold from being shaken around with the ice, yet the strainer leaves behind the extra ice, along with the rosemary or whatever else you decided to hide inside.
Make another one and share with your friend.