Declining to bar Trump from a general election state ballot on a challenge under the 22nd amendment counts regardless of legal reasoning (political question, states have sole authority, etc).

If there is, as is likely if Trump tries to run, a clear dispositive merits case at SCOTUS that seeks to resolve this, this will resolve according to the votes on that case. The rest of the rules attempt to set up rules for less-likely scenarios where this is legally decided by SCOTUS in another way.

In addition to merits rulings, the orders docket will also be considered. Denial of Certiori or Per Curiam decisions are considered to be supported except by those Justices noting a dissent. A dissent from denial of cert is assumed to be a vote for reversing the decision below, and a lack of a dissent from denial of support is a vote for affirming the decision below.

For example, if the 5th circuit declines to bar Trump, and cert is denied with 3 justices noting dissent, that's 6 votes to allow Trump to run. If they bar Trump, and cert is denied, but 2 Justices dissent from denial, that's 2 votes. Denial of a request for cert before judgement does not count, or other majority rulings that say the case is premature or lacks jurisdiction do not count, unless they effectively shut down future challenges, or result in Trump actually appearing on a ballot. A dissent on any grounds from a majority decision barring Trump counts however, no matter how technical the reasoning.

If Trump doesn't run despite no circuit case like this barring trump, this is N/A. If the 22nd Amendment is repealed before such a challenge is acted on by SCOTUS, this is also N/A.