Try setting e.style.display="none" / "" (where e is the form element object handle) to hide an element at the JS/CSS1 level. You can also use e.style.visibility="hidden" / "visible" where CSS2 is available.
Better still, wrap the form element in a
or a and modify the style.display / .visibility property of that.
@Motorollin
Strictly speaking, any element that can take a style attribute can be made visible or invisible by modifying the element's style property itself, rather than the element, which as you say, is unlikely to have a visibility property of its own.