Circuit behaves erratically when using a long cable
Circuit + LEDs = fine

Circuit + cable + LEDs = bad

The logical conclusion is that the cable is causing your problems ! No use looking at the circuits just yet although it is common sense to include all information right from the beginning. The power supply is 12V, 5A and you have a lot of LEDs. So probably a lot of current is flowing.

Let's assume it almost 5 A, for 5 A you need a decent cable for it not to drop too much voltage. What sort of cable are you using ? Do you have a voltmeter which you can use to measure the 12V ath the other end of the cable (when the LEDs are on because only then current flows).