Yes. But if the whole tail light is LED I would assume you would want the resistor on the ground wire. (This all depends on application here) Things can make this different, the amount of LEDs changes the load so the resistor values between the 2 could make it different.
I am not sure why you want to put the resistor on the green or green/white wire. Not to say you are wrong, but like I said it is all application. Do you have 2 resistors? Do you only need the extra load for 1 mode? Does the service light only look at brake/signals? (<< I don't know why they would save the couple cents to not put it on running lights though)
For example, if the running lights (less bright) use X power, then the brake lights could use 2x power (lets just use an integer to keep it simple). Your stock lights could use 10X power. This means to see the "load" your running lights could need something to use the extra 9X power for the running lights, and something to use 8X power for the brake lights. So like I said it could need 2 resistor values, one on each power wire (green and green/white)
Going off the same example as above, if there is some tolerance built into the system, then you could use something to use the extra 9x power and put it on the ground wire. This will still make it look like an acceptable load the ECU. This means it will see 11X load for the brake like, and 10X load for the running lights.
But, just to not cause confusion, there are also different ways the light could be wired internally. If the SAME LEDs are used for each mode and the brightness changes, then if you have the running lights on AND the brake lights, the the LEDs are still using only 2X power. If there are individual LEDs for each mode then it would use 3X power when both are on, and therefore 12X power if a single resistor is on the ground wire (still acceptable pending any tolerances or what not).
You can also try looking at the specs for everything. If you have a multimeter with a current function (denoted by a mA usually) then you could measure the current in each mode, and find the wattage of each mode of the original lights (with incandescent bulbs). If you do this then you could figure out how to wire it. If you post the currents and voltages here for each mode of each light I can help you figure out what resistors are needed.
Basically though just as an FYI, there is basically no way to break your taillights. I would assume they work without the resistors, which you have stated is true, so no worry there. If you hook the light up with reverse polarity then still nothing wrong, the LEDs are DIODES and only allow current flow in 1 direction. If you choose a resistor value too small, well this is impossible, as no resistor works fine, and you can't have a negative resistor. If you choose a resistor too big then your lights just aren't bright enough.
Good luck, let me know how it works out.
-John
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