Am I correct in thinking that a Non-profit LLC would only need the control prong, since you can only be granted Non-Profit LLC if the member(s) are Non-profit?

Non-profits are exempt from the ownership prong, regardless of structure. I just recommend some due diligence to confirm they are non-profit.

I've never see a non-profit LLC.

If the non-profit is registered with the Secretary of State, wouldn't a BO Form be required with the Control Person identified? I don't know that I've seen an LLC but have seen Non Profit Corporations.

There are a lot of non-profit corporations. In fact, you may find that most of them are, because the people who run them don't want to be saddled with liabilities if something goes wrong. Think of Habitat for Humanity building homes without liability protection for its board members. So if the non-profit is registered with the SOS as a corporation, LLC, etc., it's a legal entity customer and you'll need certification of a control person (since there are no owners and since the reg says you need to get the control person only).