You'll have to forgive my lack of a source as I haven't actively studied Buddhism in decades. But I was thinking that Gautama mentions it at some point. I think it comes up a lot more in the Zen traditions too.

I definitely remember Alan Watts (Not an expert on Buddhism*) saying something to that effect, but lord help me it has been a minute so I would never be able to back that up. He said that was the big secret of ego and the folly of trying to rid yourSELF of it. Trying to grab onto your sense of self would be like a light illuminating itself or scissors cutting themselves. It's a limitation of language, folks.

A lot of very good people have stopped seeking self. The radlibs told me, Chapo, how can we do this? And, folks, millions and millions of thoughts of self-doubt were behind those fears. I have those thoughts too actually. Oh yeah yeah... "Chapo it's not fair that we're winning so much." But really, folks, we let go of things we can't control. Let's make our minds quiet again!

• Actually, I think he was a learned academic on Eastern theology for what its worth

It's an idea that follows from easily from the real Buddhist basics, and is common to most Buddhist philosophy. https://en.wikipedia.org/wiki/Anatta