I never did find any more information on the official Third Eye mod, but I've been working on the controller a bit, and got it working on par with my other controllers. So, I thought I'd update this, and maybe it will help someone else out at some point, in case there are other people tinkering with out of date controllers and looking for information.
I actually fixed several problems-
First, I discovered that the voltage drop when the full throttle relay disengages was about 2v. I think the normal voltage drop should be about 1.2-1.4v, given that the Renegade uses a Darlington transistor arrangement, .6-.7v per transistor. I traced that to the wiper arm adjustment. It was set so that the wiper button wasn't going all the way to the full throttle end of the resistor, and was also adjusted so that the trailing edge of the button was contacting the resistor. So the actual contact was at least 1/8" from the end of the resistor, maybe even a little more. I don't know how many of the tiny winds on the resistor that equals, but it's enough to cause performance issues. Third Eye recommends adjusting the wiper arm so that the leading edge contacts the resistor. I did that, and also adjusted the arm so that it goes all the way to the end of the resistor, and it now only has a 1.25v drop when the full throttle relay disengages.
I would also recommend getting some very fine sandpaper (1000-1200 grit or finer), and lay it between the resistor and the wiper button, abrasive side away from the resistor, toward the button. Hold the sandpaper in place and work the trigger back and forth, so that the sandpaper polishes the surface of the wiper button that's contacting the resistor. It will make the trigger feel much smoother, and probably be less wear and tear on the resistor. That will work on any Third Eye controller with a resistor like this one.
Second, the main thing that I was trying to fix when I originally posted this, was the very low sensitivity. I found that what I would call the minimum sensitivity resistor, which sets the voltage that the controller puts out to the car when you start to pull the trigger was 100 ohms. I have no idea whether that value was used when it was new, if that was part of the lower sensitivity mod, and Howard Smith did that, or if someone else has been tinkering with it. The controller has a sticker on it indicating that it has been refurbished by Third Eye, but it's certainly possible that this was someone else's doing, not an official mod. I've attached a picture of the resistor. It's the one on the left, just under the brake pot, just above the wound resistor. My replacement is blue, not tan like the others in the controller, so it's easy to spot. The resistor pads where I have my resistor installed had resistor legs still soldered in place, but the resistor had been clipped off, and the 100 ohm resistor was soldered to the set of pads just below it, which are connected to the same traces. I swapped out the 100 ohm resistor for a 240 ohm resistor that I had on hand, and that brought the starting voltage from well under 1v (I don't remember the exact voltage, since I didn't make a note of it) up to 2.3v, and the controller now seems to perform on par with my other controllers. I compared it at the track to the Difalco that is my main controller, as well as an older Ruddock, and I can run lap times within a few milliseconds with all three, so I'm calling it fixed. Each of the three controllers has a bit of a different feel (which is probably why some people prefer one over the others), but I'd say that the repairs were a success, if I can run that close lap times, since I was down several tenths with the Renegade before the repairs.
The third thing I changed was the trigger pivot. I replaced the stock pin with a Difalco trigger pin and bearing kit. In my opinion, that and polishing the wiper button surface the best things you can do to improve the feel of a Third Eye controller. It will remove the side-to-side play from the trigger, which will allow you to adjust the wiper arm so that there's minimal pressure against the resistor, which reduces friction and makes the trigger pull feel much smoother. It should also reduce wear and tear on the resistor. I've done the same thing to the Third Eye Hitman controllers that my two sons prefer, with similar results. It's very worthwhile, in my humble opinion, and well worth the few dollars for the kit. I'd recommend it for any controller.
That's a summary of what I've done. Again, hopefully it will be helpful to someone else looking for information that I couldn't find elsewhere.