It isn't just Sigma Octantis, it is all the stars in the south, even the sun during the southern summer.
They all appear to circle a point due south.
You can't get that by just adding in 5 lighthouses.
You would need entire sets of stars, and then you need to address why no one has ever found a point where there are 2 such regions of stars observable.
Also, with how you have drawn it, it wouldn't always be due south.
So still no FE solution.
NO, and you are wrong again. Most are Flat maps and people are made to think they are projections of a Globe. The Gleason Map has Antarctica surounding waters' edge. Get use to it!
There are basically no flat maps.
Instead there are plenty of projections of the globe which people present as a flat map.
The Gleason projection was even labelled as such.
Only you can prove to yourself Earth is not a Sphere.
Sure, it isn't a perfect sphere, but no sane person thinks that.
I have proven to myself beyond any sane doubt that Earth is round.
It seems no one is capable of proving Earth isn't roughly spherical, most likely because it is roughly spherical.
In the following video a Flat Earth claims someone is faking southern star trails with northers trails. The location is Sydney. What are your thoughts? Is he right?
I wouldn't be surprised if a FE decided to fake it so they could expose it as a fake.
But I am yet to see anyone do that with the very real and observed star trails.
If they are videos, you can see what the stars are and tell they aren't the northern stars.
You can also do that to some extent with a picture, but it is much harder.
What Southern Star trails (videos) can I trust are real?
If you want to play that game, go and observe them yourself.
In fact, if you aren't too far north, then go and get a camera with a very wide angle lens (or fish eye lens), and set it up pointing due south (geographic, not magnetic) pointing an angle downwards equal to your latitude (e.g. if you are 30 degrees north it should have an angle of dip of 30 degrees). Then take a timelapse. You will observe the same star trails.
You don't need to be in the south to observe the southern star trails. You just need to be south of the equator to observe the south celestial pole and have the stars circle below it.