I finally heard back from Tascam on the GPI ports. The info received from Tascam indicate that the GPI ports are triggered not from the buttons, but from the LEDs above the transport buttons. So, if we're using the HUI protocol, we need to have the mixer connected to a computer and also need to set up the Machine Control List on the mixer with a controller that is properly configured so the transport LEDs work. The response goes on to say that once the transport LEDs work properly with HUI, then the GPI ports will also work.
Unfortunately for me, it still doesn't work for in Pro Tools. Mbuz reported in an earlier post that he also couldn't get the GPI ports working with the transport buttons in Pro Tools, though he did get working properly with Cubase. This strongly implies the problem is with the HUI protocol, and Tascam told me the Mackie protocol is both newer, and works well with most DAWs. However, it doesn't work at all with Pro Tools.
I've had the transport buttons (and their associated LEDs) working with Pro Tools since I purchased the mixer over 4 years ago, so that has never been the problem with the GPI ports on my end. Perhaps I can change something on the Machine Control List to get it working, and I am going to try. However, there is a rapidly growing possibility that the several suggestions from other posters about getting the USB-driven Punchlight might be the only solution for us PT users.
I'll post the results of my testing with Machine Control List changes. After that, I'll either have it working or will pursue another solution, such as the Punchlight.