OK, I don't think you're on the right track. Pardon for yelling but you need to see this:
YOU CANNOT EVER PUT TWO LEDs IN PARALLEL, ALONE OR IN A STRING, WITHOUT A SERIES RESISTANCE.
Attempting to parallel LEDs without an appropriate series resistance for EACH LED or series string results in large current imbalances due to mfg or temp differences. Basically you put 2 or 10 in parallel one will take all the current while the others get less or fail to turn on at all. The bright one will quickly degrade and/or burn out. This is inevitable due to the sharp IV curve and the negative temp coefficient of forward voltage. Even if they appear to be of equal brightness initially, once one gets slightly warmer than another its IV curve shifts down so it draws more current for a given voltage. They all have the same voltage being in parallel so it ends up taking more current, increasing its temp and increasing the instability.
Your forward current is probably too high. A 5mm pkg can take 20mA for awhile but not all that long. Many LEDs in a small area increase the heat and the voltage source is inconsistent so let's go with 15mA (even then that's pretty high!).
With a 12V source, you can put 4x 2V LEDs in series = 8V forward voltage. Now the car's say 13.8V when running, (13.8V-8V)/0.015A = 387 ohms. 87mW per resistor. On paper it seems like you can put 5x in series, even 6x, but there's not enough ballast resistance for a poorly regulated source voltage. The current will vary widely from 12.8V with the engine off to 14.2V or more that the wires might carry under worst conditions. 14.6V is possible.
So you need to parallel 240 strings of 4 series LEDs and 1 resistor per string. That's 240 resistors. Sorry that what you have made isn't right but it's not workable.
Why 960 LEDs, anyways?? I've seen LED taillights with like 20 or 30 per side. 960 is absurd, not sure what you're going for. Doing this with 20 or 30 is nowhere near as complicated to make!