You can spot Base64 encoded JSON.
The PEM format (that begins with `-----BEGIN [CERTIFICATE|CERTIFICATE REQUEST|PRIVATE KEY|X509 CRL|PUBLIC KEY]-----`) is already Base64 within the body.. the header and footer are ASCII, and shouldn't be encoded[0] (there's no link to the claim so perhaps there's another format similar to PEM?)
You can't spot private keys, unless they start with a repeating text sequence (or use the PEM format with header also encoded).