Hiding cursor with t_ve in terminal

Vim's documentation lists 't_vi' as "cursor invisible" and 't_ve' as
"cursor visible", but provides no hints on usage. Naively, I would
have guessed that Vim would send the 't_vi' sequence when you somehow
indicated that the cursor should be hidden (e.g., using something
analogous to 'guicursor' for terminals), but there doesn't appear to
be any such mechanism. The only way I've been able to hide the cursor
in a terminal is to make the "cursor visible" option empty: e.g.,

set t_ve=

I interpret this behavior as follows: when you tell Vim there's no way
to make the cursor visible, it immediately uses the 't_vi' option
value to make it *invisible*. This was less than intuitive to me, and
I didn't see it documented in the Vim help. Is the behavior
well-defined? Can anyone give a better explanation of what's happening
and perhaps the rationale behind it? Have I simply missed the
pertinent documenation?

Thanks,
Brett Stahlman

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