New Sol List Can I Apply For A Work Visa In Australia If My Position Is Not On Skilled Occupation List (SOL)?

Can I apply for a work visa in Australia if my position is not on Skilled Occupation List (SOL)? - new sol list

I am an American in my twenty years who qualify for working holiday visas. I think I want to give to Australia and we hope that there is a company that describes me or sponsor of an immigration visa can request to be independent. He currently works as a recruiter I see in the list of SOL. Am I still eligible for a visa? If not, there is another application to apply for a work visa?