Light is not the same thing as gravity.

If the sun vanished we'd be flung out into space immediately. We wouldn't see the encroaching endlessness of a sunless sky for about 8ish minutes after the disappearance.

We'd feel the effects of the moon's missing gravity immediately, as gravity is not affected by light.

A thought experiment for you: what if, in this scenario, the moon had risen on the opposite side of the planet (from you) when it vanished? Or, conversely, what if it was a new moon that particular day?

Another interesting one, perhaps more to the point: does the moon stop pulling on the planet when you can't see it? Well, no. The mass of our moon is still present even if it's not visible, and the mass of an object is what influences said object's gravitational pull.