The neck packing issue is good to be aware of. One can have the neck neutral (spine bent neither forward nor back at the neck) or slightly extended (spine bent back at the neck) while keeping the neck/upper back "packed".
The picture that Kenny shared shows excessive neck flexion. The feeling of packing the neck is like rotating the skull forward without bending the neck forward. If you keep a "tall" spine all the through the neck, but then kind of try to form a "double chin", where your chin is pulled into the front of your neck, you get an exaggerated version of neck packing, as long as you aren't rounding your neck forward to achieve it. It can be counter intuitive at first to keep neck neutral or even extended while keeping the chin tucked.
You can have your neck flexed forward without neck packing (like in the picture), but you can also have your neck extended back without packing, where you end up with two exaggerated curves in the upper back/neck, one for the flexion of the t-spine, and another in the extension of the neck. That's the "computer" posture that many of us need to get out of.