I am going to say that my reading of the spells leads me to the ruling that the invisible character can see themselves but if you've read them yourself and don't agree I doubt I can sway you, since it's not specifically addressed.
Pathfinder Design Team wrote:
Invisibility: Can you see yourself when you're invisible?
The spell doesn't say one way or the other.
Because being invisible doesn't give you penalties on actions that require you to be able to see exactly what you're doing (such as picking a lock), you can assume that you can at least see yourself well enough to perform such actions without penalty. Whether this means you can see yourself as if you were not invisible, can see yourself as a ghostly image, or some other description is up to the GM, so long as the description doesn't hinder your own actions.
So at first it doesn't seem helpful, but at the end it's basically that it shouldn't interfere with your own actions, so if you have a scroll on you as you turn invisible you should be able to read it, if you have a wand, you're probably not going to point the wrong end at yourself, if you have a hammer you can probably hit a nail (and with the flat head, not the claw), you don't have to try and guess or roll randomly when you attack with your double-weapon quarterstaff to hit with the end you enchanted at +2. So just assuming that you can see yourself and your things is likely the best ruling you should make.
