Suppose I have a power supply with 2x12V cables. The 12V has been split into 2 inside the power supply. What happens if I join these power lines together in parallel, from an electrical properties point of view? What effect will this have on the power output?
Without a datasheet or knowing exactly how these two 12 V output wires are connected internally, don't connect them externally.
If they are merely connected to the same 12 V supply internally, then connecting the two external ends just puts the two wires in parallel. That does no harm, but probably little useful either. Presumably the wires were sized to carry whatever current the power supply can deliver, so two of those in parallel will only lower the voltage drop a little bit.
If the two wires are derived from separate supplies inside, then connecting them could have unpredictable results.