First of all... If you can afford a 'Vette, you can afford a newer, better, more capable, more reliable computer for your ride than an Infill T3.
The store here sold them, and the majority of users reported problems.
I would hardly classify the T3 as "awesome".
Honestly, it sounds like there are more problems with your 'Vette than just the stereo. From your description, it appears that someone has altered the electrical system. For safety and reliability, I'd take it to a GM dealer and have them look into the problem. If the previous owner jacked up the electrical system, I wouldn't expect it to be a cheap fix.
As far as the wiring for your T3, the EASY way to wire those three is as such:
Constant 12v straight to the battery (+) terminal
Ground to a grounding point on the chassis or the (-) terminal on the battery.
ACC 12v to a line that is on when the ignition is on. Typical ACC sources are the radio harness, cigarette lighter, or an ignition-controlled circuit in the fuse panel.
As far as finding various lines to tap into, The 12Volt has wiring information for a lot of different models.
You say you have a service manual, and it should contain the same information, as well.