Hello.
Maybe I can help a bit.
I'm a man, and occasionally a transvestite, or crossdresser. The label is unimportant really. I imagine that there is as wide a range, or spectrum of gender dysphoria as there is between heterosexuality and homosexuality.
At one end, you have men who believe, and have believed all their life, that they should have been born a woman, and at the other you have men who feel happy, or even sexy when they wear womens clothing, usually in the form of lingerie - society sends men some pretty strong images and ideas about the sexualisation of clothing from a pretty early age, so you can see where that comes from, but in my experience it's triggered by some aspect of their own sexual identity first.
It is horribly difficult feeling like this, because it isn't "normal" - and the one thing that you want to be is accepted as normal in this state - the gay community temds to be a bit sniffy unless you are a proper screaming drag queen, and very, very few women want to think of their partners having such a side to them - it's not really about a feminine side, it's about an image of femininity that probably only exists in the minds of men.
If your husband has been going to gay clubs, it's perhaps because he feels a bit more accepted there - it's a community that is a bit more tolerant (though not always) of people who aren't obviously in the mainstream, and transwhatevered people aren't numerous and out enough to merit their own places, so they put their lot in the with the queers and the dykes, and good company they are too - though you find that if you go to any club dressed up it is ALWAYS the men who hit on you, because they assume you are gay - and they always start their chat ups with "I'm not gay but...".
You've got a choice. You can talk to him about it, and try to understand it, and maybe accept it, or even relish it. Or you can let your fear take hold, and tell him you think it's weird and wrong, and he's gay, and you want him to stop, and he will tell you he will, but he will never be able to, not really, so he'll either keep it a closer secret, or you'll catch him again.
He's as likely to be gay as the next man, crossdresser or not, but maybe, if you drive him away, or into hiding, he'll turn to someone who accepts him for comfort.
Why would you look in the glove compartment - if the answer is ordinary, then maybe he meant you to find them. Can you imagine, for a minute, how difficult it would be for him to broach this subject with you? When would you expect him to do it - when you first meet, when you get engaged, on the wedding night, when the children take their first communion? I don't think that there is a right time for it.
There are a few good organisations that can offer you help - not him, but you - if you feel uncomfortable.