Cleon
Legend
I'm with Shade. The "recharge time" reminds me of a breath weapon, which is also Con-based.
In fact, here's a take on the ability based on a breath weapon. I'm trying to make the recharge time a bit more standard 3.X, but as compensation I'm changing the bolts to lines of electricity. All open to negotiation.
Lightning (Su): A stargazer can unleash two 30 ft lines of electricity from its eyes, which do 6d6 electricity damage each (DC X Reflex save halves). The stargazer can use this attack every 1d4 rounds. The save DC is Constitution-based.
That looks OK to me.