"What factors determine eligibility for this situation?"

The search results you will get include IRS guidance for how foreign income is computed for purposes of retirement account eligibility. Did you do that search and read some of those topics?

google: are foreign earnings eligible for ira

Results include IRS links. Did you want that copied and pasted here, or perhaps it is more useful to read them yourself, and perhaps bookmark those that are good reference for you to use later.