OK, voltage, current, and resistance are all related by Ohm's Law:
V = I * R
A current flows when there is a voltage across a reasonable resistance. With no voltage across a resistance, there is now current flow. Likewise, with no current through a resistor, there is no voltage drop. You are right, the computer is probably not measuring the resistance of the tail light, but rather the voltage. The computer might think it needs 12V to "overcome" the resistance of the stock tail lights. When you put in the LED's, the resistance might be much lower and the computer supplies less voltage to overcome this resistance. If this voltage is not what it expects, it throws an error. This may be an over simplification of the system, but it is probably a safe assumption as to how it works.
Since we cannot change the source voltage, the only thing we can do is to try and match this resistance. I'm not doing this mod, so I cant really do this myself and give a definitive answer on what seems to work.
I do know a little about DC circuits though, so I can try to help.
Also, resistors are measure in Ohm's, not Watts. If a resistor value is given in Watts, something else is assumed, possibly maximum current.
P = I * V --> P = I*I*R
In general, when using an LED in any DC circuit, you must use a resistor in series with the LED to limit the current or it will most likely burn. There is probably a resistor in the LED assembly to keep them from burning, but its hard to say if the manufacturer matched the resistance of the stock assembly.