On a boat in the ocean at the equator (earth rotating 28km) watching the sun dip below the horizon (4.7k away) do we see any photons that were emitted directly from the sun (8 minutes ago) or are they all reflected off of something? My Gedankenerfahrung
We see the Sun with a time delay of a little over 8 minutes (about 490 to 507 seconds). So the location that the Sun appears to be now is actually where it was 8 minutes ago. In a comment you said:
I'm thinking about the photons that left the sun when it was above the horizon but now we have rotated and it is below the horizon. Since it takes 8 min to get here are there any photons in that "eight minute stream" that reach our eyes before the sun disappears below the horizon (i.e. from the "stream" while sun is not currently visible)
You see all the photons in that "eight minute stream" (assuming that stream consists of photons heading in the direction of your eye). Those photons continue to travel in a straight line towards your eye, the rotation of the Earth won't affect that.
However, all of the above assumes that light always travels in a straight line. But that's not actually true: the path of light can refract (bend) when it changes speed. The speed of light in air is lower than the speed of light in a vacuum. The exact speed of light in air depends on the air's temperature, pressure, and the amount of water vapour in the air.
The light from a celestial body near the horizon passes through a lot more air than a celestial body that's high in the sky, so refraction effects are greatest near the horizon. Atmospheric refraction causes the celestial body to appear higher in the sky than it would appear without air. Coincidentally, the amount of refraction at the horizon is roughly equal to the Sun's apparent diameter. So if you can see the lower limb of the Sun just touching the horizon, if all the air disappeared at that instant the Sun's upper limb would be on the horizon, i.e., the Sun would be on the point of setting.
For more details on astronomical refraction, please see the Wikipedia article on atmospheric refraction.
If you can see the sun, you get photons direct and also reflected or scattered photons. There is an infinitesimal delay caused by the fact that light travels more slowly through air than it does in a vacuum, but the delay is so minute that it is hardly worth mentioning. Nobody except for astronauts sees the sun without some atmosphere getting in the way, and it's a good thing it does. At sunset and sunrise, you see it through a maximum thickness of atmosphere. After the sun has gone below the horizon you will only see reflected or scattered photons.