good luck sorting that out. Clear line of sight ... its in the Himalayas.
Maybe we could choose a different mountain? Do you think it would be possible to find a scenario where we have a clear line of sight to something really big, but also really far away? Something we could test this out with?
Off the top of my head, how about Mauna Kea? It's 13,803 ft sticking more or less right out of the ocean. How about we sit in a boat 300 miles off shore and look at it? At 300 miles, I figure Mauna Kea should be 0.5 degrees tall. As long as we're careful to observe from high enough to see over any potential waves... cruise ships are easily 200 ft tall, and cruise ships go to Hawaii all the time. Should work right?
So, you want to take me to a far flung destination on a boat with you to "look at a mountain and see if we can see stars behind it"? Let me guess, I'll need to go to the hand rail and lean over and peer at the mountain waiting for the cosmic alignment?
I fell for that once before on this forum. I ended up going to a basement in Ohio to help some large guy with his rocket. He insisted I polish it and help lighten his payload. When I got there ... there was just a stained mattress and no space stuff.
Alas, you have seen through my ruse!
But seriously, don't you think that would be a really good, really conclusive experiment to try? If you see the star, the earth is round. If you see the mountain, the earth is flat. If you can't make out the mountain, but something is blocking the star, we have good evidence that the earth is flat.
That's science, baby!