I have electrons in place of white blood cells.
I think you should hook it up exactly as it is says to hook it up and DO NOT, i say again DO NOT deviate from that.
Red wire to a +12 source that comes on when your old dash lights would come on. This would be the parking lights or the +12 into the old dimmer. You can not
use the output of the old dimmer. You can not use the old dimmer to control the new lights. You want a +12 source that is hot when the lights need to be on and nothing more.
Black wire to a ground. Self explanatory.
The new dimmer it came with is now the only thing you can use to control the dash light intensity. That dimmer is a potentiometer (variable resistor) which is connected to the circuity inside the black box. You can not connect it to something else. Find a nice place to mount it because your stuck with it. Or you could set it for a nice level and hide it somewhere. But it has to be connected and you can't substitute something else.
The black box is likely a VOLTAGE REGULATOR. It is not inverting or converting anything. It is regulating the voltage and current to the LED's that backlight the gauges. You can not just simply pump variable voltage into LED's like you can with a light bulb. So that black box is probably taking your 12 volts in, regulating it down to 5v and varying the current based on your new dimmer **** setting.
If the thing is installed correctly like this and it still doesn't work right, then it is broken or its just junk. This can be expected when you buy on eBay. Sucks but thats life.