Nonono, sure the LIGHT is not invisible. But YOUR eyes are. The way humans see light reflects off a surface then is gathered by the eyeball. It is focused by the lenses then projected upon the back of the eye. IF you are invisible the visible light instead of being reflected within your eye passes right through. Therefore, you are blind.
This is a somewhat garbled version of the facts.
Vision relies on two things -
refraction of light by the lenses of your eyes (and spectacles if you happen to need them) and
absorption of light by the retinas in your eyes (For the sake of brevity, I'm taking as given the bits where the light energy is converted into nerve impulses which are in turn processed by the visual networks in the brain to yield qualia in whatever passes for awareness in the mind of the beholder

).
In order for something to be visible, it must
reflect,
refract,
absorb and/or
emit light in some fashion. If an object does any one of these things, then it is visible (to any creature sensitive to the affected wavelengths of light). If it does none of them, then it is invisible - and competely blind.
But all of this, while interesting, is completely irrelevant. The spell
Invisibility is listed as
Illusion (Glamer). Illusions affect perceptions, not reality. If you wanted to get all pseudo-technical, you could say that the subject is surrounded by a fog of magical energy which causes viewers to discount whatever it surrounds. Kind of like an SEP field.
The rules state that if "
... the character casts the spell on someone else, neither the character nor the character's allies can see the subject ..." This says nothing about what happens if the character casts the spell on himself or herself (or itself), but the very fact that they go to the trouble of mentioning what happens when you cast
Invisibility on something else, implies that you would normally expect the caster of a glamer to be immune to its effect. What they are saying, albeit elliptically is that it is the
subject of an
Invisibility spell that is immune.
In other words, the subject of an
Invisibility spell
can see itself and any equipment it carries. If you want to rule otherwise in your game, that's fine with me, but don't use fallacious arguments to back up your case.