I’ve got a few old trade caps that I wear under my (road) helmet when it’s raining. Keeps rain out of my eyes and my bald head warm, whilst giving the ‘grizzled old pro’ look.
I’ve also got a genuine yellow Campagnolo cap from the 1991 Tour de France that I had to fight an old French lady for. Far too valuable to ever wear.
If you do wear one, try to look like this :
Not this :