There's three ways to do this, the proper way, the harder way or the half azzed way. The way its hooked up now is not the proper way. Its the half azzed way. Unfortunately this is the way quite a few manufactures chose in the past. I had never seen it used the way yours is, it was done to change the speed of turn signal flashers.
The proper way is to swap out the tail light assembly with LED's of the correct output. Obviously the one's you have are not. Based on your posts, this is not going to happen.
The way your doing it now, your using a resistor to consume power, limiting it from the lights. The resistor will change the power to heat. If the resistor wasnt big enough, it most likely would have already burned out. You can remove the resistor, test it and get two that are double the resistance rating, hook them in parallel and split the power between them. The problem is though, the same heat will be generated, just split between them. This will not remove the heat issue.
If your going to keep the tail lights, how you should be doing it is an inline regulator, not a resistor. A pulse width type would be best. Now you can hook it up, adjust to whatever you want and just hide it in the rear quarter. The module will most likely be 3X1x1. These run somewhere around $20.
Here's one I just searched out. This ones a bit overkill and I would look for one that doesn't have the switch hanging off it. It’s a start.