That is a Smartwheel SM209 Control box. Plug J12 is like what was said goes to your headlights and those wires maybe discolored from heat but in electronics that is not burnt and is probably normal. Seen a lot worse and it keeps on ticking.
Now as far as the cruise control it appears that the Smartwheel is maybe working OK and it maybe a problem in the engine ECU but there are some relays inside that box. It is the ECU that is in fact the cruise control. Since the Smartwheel is sending the command for fast idle OK means that it is communicating with the ECU and that one button you hit for increasing the idle speed or setting the cruise control going down the road is the same button means that the Smartwheel is OK.
So using the Cruise Control Buttons you can
1. On/Off Button - turns the cruise control on and off OK (we know this because you have fast idle) so that is OK
2. Res Button - it works ok because you can push it and get fast idle. It is the engine ECU that slects the speed for each push of the button. So that is OK
3. Set Button - Here is the problem is that it does not set the speed going down the road and there is no way to test it sitting still other than with a multimeter doing the test below which checks out the box and the relay.
You need to go to page 7 of the Smartwheel trouble shooting manual and do the Cruise SET Test with a multimeter.
http://www.vipwheels.com/PDF%20FILES/TROUBLESHOOT.pdf
If it passes that test then the problem can be in the Engine ECU or the plugs or cables going back to the ECU.