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I discussed the problem with wiring trailer hitch lights in my last post. The main issue being my car has separate bulbs for the brake and the blinker, where the trailer uses the same bulb.
 The solution requires first thinking about the logic of how the lights work. When the brake is on both lights are on, but when you turn the blinker on you need to detect that the light is now in blinker mode so it will turn off a light that is already on. In addition to this you then need to realize when the blinker is off so that it returns it to brake mode. While this could be done with logic circuits or a micontroller that is way too complicated, and I didn't even explore it.
The first thing you need to realize is that the easiest way to make the lights blink when the brake is on is that you need to reverse the blinker function when the brake is on. That is if the brake is on and the blinker is on, the blinker light on the trailer will be opposite what the car is. The reason for this is simple, it's easy to detect when the blinker light is on and shut off a light so it blinks, then it is to actually change functions.
Once you realize the logic of the lights you will see what you are looking for is the function of an XOR logic gate. That is if the brake is on the trailer light is on, if the blinker is on the light is on, if the blinker and brake light are on the light is off, and if both are off the light is off. Which brings me to the first solution which uses an xor logic chip and output transistors which someone has a patent on, although it can get a lot simpler than that.
 The goal now is to make an XOR logic gate with transistor logic and a decent power transistor in the final stage. This leads us to our second design which I am sure we can find many which all basically do the same thing.
The above solutions work and aren't all that costly but there is a reduction in part count and cost that can be made if you realize a little trick about how the car is wired
If by some miracle the car wiring put voltage when it was on and connected to ground when off, then the circuit would include no parts. We could simply connect the trailer bulb between the two positive sides of the brake and blinker light and it would work. The problem is most cars I know of don't pull the high side to ground when off, but they do pull to ground sort of. The high side isn't really  pulled to ground when off but it is connected to ground through a resistance, and that resistance is the bulb in the car. If you were to connect a light between the high sides of the brake and blinker, you would get the desired function from the trailer light, but it would also light the car blinker light when you put the brakes on and visa versa, which is no good at all. While this isn't good, it  does provide us with something useful, and that is it pulls to ground, just that we can't put much current through that or we will light a bulb we don't want lit.
So now we come to the final solutions, the first of which uses a relay and some resistors in between both bulbs. These solutions may not work with a car that has LED bulbs, but a little resistance in the circuit could fix that. To me using a relay isn't desirable, they aren't that cheap, and I don't like having moving parts when I don't need them, but it works and is used.
The last solutions I have both use PNP transistors or in practice a PNP Darlington transistor. In a PNP transistor if the base is lower than the emitter voltage then voltage will flow from the emitter to the collector. If the base is equal to or above the emitter voltage, then nothing will flow between the emitter and collector.
This is useful because we can use the  ground through the bulb at the base and the positive voltage output at the emitter to form a voltage difference. When the bulb is on however it is at the same voltage and the output is off. Based  on this I have a couple circuit designs, which I think are fairly simple.
I guess you have to deicide what you think the best design is, for me I prefer either of the PNP transistor solution, this is based on the price of components and the simplicity of the design.
Some of the images (the ones with numbers) come from patents so I am refrenceing them here if you want more info 5701116, 3970860, 5030938, 4751431, 6177865 B1 The other images are from coworkers and myself.
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