I think this sort of negative definition is not very useful, though. As soon as telepathy is demonstrated, it becomes an existing sense. And that's not just word chopping, it's pretty evident that this is going to bother people and that they will believe it can't be "real" telepathy.

In a non-trivial way, this means that "telepathy" is defined as something that does not and can not exist. If it exists, it won't be telepathy, because it'll have to be something real, and as such, it won't be "real" telepathy.

If you do give it a concrete definition that permits it to exist, it is often the case that it turns out that we have it in the real world already, unless you define it as some sort of ability to invasively read people's minds or something, in which here's hoping it never exists in this universe.

Is intuition a sense - or is that potentially some people excelling at reading physical cues that 99.999999% of people can't see or relate to what someone is then likely thinking?