With that example on ghosts while yes in that scenario it is instinctively put on the one who says ghosts don't exist when the person claiming the exist provides evidence the person claiming they don't then would naturally respond with there own evidence thus both sides provide evidence.
The side claiming that ghosts do not exist need only to look around and say "I don't see any ghosts," and thus the evidence for their non-existence has been provided. This is why the burden of proof is primarily on the people claiming that ghosts do exist.
Similarly, Flat Earthers need only to look at the world and say that it looks flat, and thus evidence for the flatness of the world has been provided. The burden of proof is primarily on the people who look at the world and claim that they see it to be round.
Hmm. But isn't that like me saying "I don't believe in kangaroos, I have never seen any kangaroos".
I could then say that the burden of proof lies with people who claim they do exist.
The difference between kangaroos and ghosts of course is it would be quite easy for people to show me photographs and film of kangaroos and probably arrange a visit for me to see one - in my part of the world that would be in a zoo. The burden of proof would then lie with me to show that all this evidence is wrong.
To relate this to FE/RE I think it's fairly reasonable for someone to look out to sea, observe a flat horizon and conclude the earth is flat unless demonstrated otherwise.
The RE response though would be "look at all these photos/film of the earth from space and the testimony of all the people who claim to have been to space, look at these photos which show distant buildings occluded by the curve of the earth, look at all these observations which fit models of a spherical earth...etc etc".
The burden of proof then lies with FE to demonstrate that all this evidence is wrong/fake and that a flat earth model can explain all these observations, no?