Yes, this is gluten free
Distillation leaves gluten protein behind, so spirits are gluten-free even when made from wheat, barley or rye. FDA verifies this category by confirming the absence of protein. Flavorings added after distillation are the only thing worth checking.
Fermented liquid boiled and recondensed. What crosses over in a still is alcohol, water and volatile aromatics; what stays behind is everything heavy, and protein is heavy. That single physical fact is the whole answer for the entire category — whisky from barley, vodka from wheat, gin from grain alcohol.
Because the starting material is openly a gluten grain and says so on the bottle. Scotch is barley. Rye whiskey is rye. Many vodkas are wheat. Somebody who has learned to read for grain names finds them in enormous letters on the front label, and the instinct to put it down is a good instinct applied to the one case where it does not hold.
Plain spirits are fine, and that includes the ones that sound least fine. Where to actually look: flavoured and cream liqueurs, anything with a colour that did not come from a barrel, and beer-based or malt-based pre-mixes, which are not spirits at all despite sitting in the same fridge. Worth knowing that a persistent reaction to a spirit is more likely about the mixer, the garnish or the shared bar equipment than the distillate.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.