For me India joining the F-3 project as a junior partner would benefit both parties.

What can India offer Japan? A contribution to development costs, cheaper development engineering (where India has the know how to undertake development tasks), cheaper production and assembly and a larger production run, possibly making F-3 sufficiently price competitive to win export contracts.

What can Japan offer India? The technology (or ability to develop or acquire such) to actually build the F-3, decision making discipline, organised project management etc

On the political level both India and Japan are unsettled by China’s rise to prominence.