I have a spare dishpan and rack under the sink, with other sink-y needs in it. I drape the gloves over the edge. I have no problems with moisture, but then the cabinet isn’t sealed, it has a gap below the sink, so there is some air in there.

Perhaps you could add a drawer handle inside the cabinet to use like a towel bar, but for the gloves?

I’m also a dish glove user, even though I use my dishwasher for almost everything. I can’t STAND touching dirty dishes with my bare hands, and I don’t ever really clean anything with bare hands. Some of it is sensory for sure, and the other is that my skin is too darn sensitive and even most naturally minded cleaning products still make my skin break out. (I even use gloves when hand washing clothing) I always tend to have a plastic bin under every sink in the house and I drape my gloves over the edge of those, wet part inside the basket and glove opening over the edge of it. I don’t like them on the counter or over the sink edge because they invariably get knocked into the sink and then I have nasty, wet gloves, plus I don’t like the look.
I bring gloves with me when I travel too. I use disposable gloves when handling meats and when cutting most fruits too because things like pineapple, mango, and cantaloupe make my hands itchy. Where I work (I’m a barista) I keep my own soap and gloves as well and only use my bare hands if I’m using a rag with hot water to wipe things down, gloves come on for ANY chemicals and sani bucket use.

I have a small towel bar mounted on the inside of the cabinet door under the sink and they hang on that.

Good idea to have bins and gloves under every sink. Thanks!

I hang mine on the inside of cabinet door under the sink.

I usually hang them on the faucet to dry and then put them in a drawer next to the sink after. I like the idea of adding a small towel bar, but that unfortunately wouldn't work in my kitchen.

I clip them into a Command clip stuck to the inside of the cabinet door below the sink.

Bluebell, well I had not heard of those Command Clips!!!! That's great. Thanks.