Unfortunately distillation doesn’t guarantee gluten free or more specifically the small amino acid chains (gliadins) in gluten that are the culprits.

If this was actually the case then all distilled alcohol would taste exactly the same… And chemically be the same but alcohol and water are azeotropic … You can google that … But it means no matter how many times you distill you can Never end up with a pure liquid. In,practice it means that according to funny things like the weather (air pressure) the final product will vary.

Rather sadly the lower quality ones possibly are safer …. Than the artisanal whisk us for example …it’s also a bit unknown how the gliandins will enter your system in the presence of alcohol … The definition of a proclamine such as gluten is that it is soluble in alcohol.

That’s not saying it will constain glaidins but no chemist I know would guarantee it doesn’t… Unless you start with a non grain one like tequila or rum ….
That said years of experience tells me gin and vodka are usually ok…. Tequila and mescal you are better sticking to the adult versions anyway as someone else said ..

Don’t shoot me it’s just chemistry.

Rather more sadly for the OP I found it increasingly difficult to get properly hammered without a hangover as my coeliac has progressed. It’s less about a headache than my digestive tract … And many have nothing to do with the gluten and more to do with having a wrecked digestive tract.

Decent red is usually good, can’t stomach champagne or anything Sur lies (like muscadet)