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If the sun disappears when? According to GR's conception of simultaneous events, it disappears immediately.
Which two event are you talking about being simultaneous? The Sun going out and Earthers observing it? Those things will not be simultaneous in any reference frame, because they are "light-like" separated. (ie they lie on a 45 degree line in a Minkowski plot.)
I think what he means is when the light from the sun disappearing arrives at earth, that’s effectively when the event of the sun disappearing happened from the earth’s perspective.
wait, who's he?
Yep. Imagine you’re off in space such that you, the sun, and the earth make an equilateral triangle. The sun disappears, then after 8 minutes you see it disappear. Then after ANOTHER 8 minutes you see the earth go dark, because that light had to cover two of the 8-light-minute long legs of the triangle.