> I've been told that it's effectively a mental illness if discovered during childhood (as is ambidexterity). Yet I can't help but think that it is not a mental illness, but rather something else.

https://en.wikipedia.org/wiki/Handedness#Types: “Mixed-handedness or cross-dominance is the change of hand preference between different tasks. This is about as widespread as left-handedness.”

⇒ about 20% of the population is not strictly right-handed. That’s not a majority, but I think the word to use for that is “normal”.