Combine the seltzer water and olive juice in a medium microwave-safe bowl. Sprinkle the gelatin on top and leave it to bloom for 5 minutes.
Microwave the bloomed gelatin mixture until dissolved, about 30 seconds. Stir in the vodka or gin and dry vermouth. Divide the mixture among twelve 2-ounce glasses and place an olive in each glass. Refrigerate until set, at least 3 hours.
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