BNE flights departs from T4 gate 41. It usually arrives at TBIT.

However, which terminal you arrive really doesn't matter because you are dumped outside security after customs so TBIT OR T4 doesn't make a difference, you have to go thru TSA at T4 at peak hours in the morning when there will be hundreds of AA frequent flyers with precheck slowing down the line.

Also due to construction at TBIT, there is also a chance that any 747 flight will be directed to the remote pad and you will be bused in to TBIT for processing, which will add about 30 minutes to the process.

I would not attempt any connection with less than the required 2 hours.