Hmm, wouldn't Detect Magic work almost as effectively then? Assuming that See Invis isn't targetable...
You cast and then have one round to study a quarter circle and lookie, magical aura there with no one visible near it.
Of course, that hoenstly is really more useful in the dungeon environment and less so the flying invisible mage (and doesn't last nearly as long, but is useful enough for finding out 'general' idea of where).
Course the more I think of it, the less effective Detect Magic is as a makeshift See Invis is.