Not sure what the issue is here, but, I've tried rooting a friends T-Mobile SGS3 on 4.1.2 using this method and I get a FAIL in Odin when pushing the PDA file to the phone.
Drivers are installed, Odin is running and seeing the phone and the phone is in download mode.
Remove battery cover and battery to get the model number. There are several T-Mobile SGS3s. Some models may not be supported.