His profession had something to do with it. He was continually creating and discarding shells. That was his work. Lots of actors have a problem with knowing who they are between jobs. Sellers had it to the max.
We mistake the shell for the self. Sellers exposes that mistake. This is why his life is so interesting- and troubling. What is a man without a shell? Nothing but a chaotic tumble of infantile emotions.
Sellers was a naked, squalling infant- but also a genius. He was nothing. Out of nothing he created a multiplicity of extraordinary people.
He was no-one and he was any-one and everyone.
P.S. Geoffrey Rush doesn't look in the least bit like Sellers- Sellers had a smooth baby-face, Rush is haggard and acne-scarred- but he has the body language so right that it's spooky.