If I have an AA flight scheduled to arrive in GRU (from DFW) at 6:25 AM, and I have to catch a GRU-IGU flight on TAM at 7:20 AM, but the AA flight is delayed for some reason (weather, mechanical reasons, etc.) and I miss the TAM flight, what will TAM do? Just put me on the next GRU-IGU flight with no extra charge/fees? (I don't have any status with TAM or AA, btw)

Does TAM have free standby? If so, maybe I could do that and just take a GRU-IGU flight later that day?

Also, how much time should I probably allow at GRU to switch from the AA flight to the TAM flight? I won't have any checked luggage on the AA flight (just carry-on).