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Something seems off there, a 2.2A current draw for 24 LEDs is a bit high, unless they're each 100mA LEDs and all in Parallel. If you made that yourself, it would draw around 500mA at most with the same rated LEDs.
Check the voltage of this 12v adapter you're using. If it's not a switching type it will be over 12v, whereas the 360 is exactly 12v and since those things were made for a car they could have been made to work at a littler higher voltage than 12v, like everything in a car is. Even though it's rated at 12v, when a car is running the Alternator will put out closer to 14.4v or so, so it can charge the battery, this also means that everything 12v in the car is getting 14.4v as well. The Red working where Green doesn't could also point to a voltage issue, since Red LEDs have a lower voltage requirement than Green ones.
They should still work on a fixed 12v though, so check your connections again. A bad solder joint or too small of a wire can act like a Resistor and it could be you're losing voltage there just enough to not make it light up, then last but not least, make sure the 360 on since there's no 12v in there when it's off.