10W LED, no need for constant current?
You have not mentioned the color of the LEDs. The typical white LEDs that make up modules like yours would take more than 3V to reach maximum rated power. I would say around 3.5V could be a common number.

For a 3.5V white LED, probably around 20% of the voltage drop is due to ESR. A LED (of the same base color) requiring lower voltage and therefore has a corresponding lower ESR would be more efficient.

So there is an unavoidable resistor in series with every LEDs already. If you use the number 12V, 0.6A, 20% ESR then the ESR = 12 * 20% / 0.6A = 4 ohms. These are guesses and may not reflect what you have. But say if these guesses are exactly right, then you would get 1A at 13.6V.

(The simple ESR model breaks down badly at low current).



Rereading what I wrote, I was assuming 4 x 3V. But there are only 3 LEDs in series, so the numbers do not add up.