In caving, the helmet's primary purpose is to prevent the wearer from knocking their head against the top of the cave. In some cases, it has to be removed especially in small wild caves (this is very typical of South Texas) and pushed in front of its owner to get through tight formations. Besides this one exception, they should be worn at all times.
If you are looking for a caving-specific helmet, look for features like headband clips for headlamps,
and other devices to hold a light in place.
Duct tape plays an important role in fixing multiple lights to a caver's helmet. You will very often see a small mag light taped on to the side of a helmet so that the wearer can see small things up close. This is especially important when studying bats or invertebrates.