Based on what the OP said, I believe your second JJ flight is JJ3510 I think the most likely scenario is "a)" as set out by pb9997. I think that most continuing international flights going onward to GIG would retain the same flight number. (At least UA does this) Also, there are 2 earlier JJ flights with numbers different that 8081 that you could take, and if an international continuation it would be the earliest one, but even that is a different flight number and a 6 hour layover. So you would clear customs and immigration at GRU.

While you would have approximately 12 hours between flights, bear in mind, as often mentioned in other threads here on FT, the traffic in SP can be horrendous. So depending on where your relatives live, you might find yourself worrying about whether you would make it bake to the airport in time. You could always ask them if they could meet you closer to the airport to allow more visiting time.