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The Earth’s rotation has little to do with the centre of the Solar system’s gravitational well? It’s basically a point under the Sun’s surface (largely thanks to the influence of Jupiter) as the Sun contains over 98% of the Solar Systems mass.
The Sun’s position (not direction) is ahead of where you see it – from Earth you see where it was eight minutes ago, and given the Earth’s rotation you are always 2 degrees behind where it is.
There are no fixed positions in space. So for convenience imagine rather than the Earth moving about 5,000 km (around the Sun) in the eight minutes it takes for light to make its journey and rotating 2 degrees whilst it does so, imagine the Earth is your fixed point in space and the Sun was in relative motion. Would you envisage it actually was where you see it?
A thought experiment for you. If every ten seconds the Earth moved a light year from our Sun, would you expect a lag in where you saw the Sun or no change?
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