Why would the blinker switch break after he added a 12V circuit?
If things burn up after you add a 12V accessory circuit you must have managed to somehow get +12V to connect with 24V ground, or the other way around. A shorted circuit. I dont think that 12V+24V (36V) would kill any of these components. If thats what happened.
Could you draw a simple diagram of how you connected these circuits? To be, the best thing would be if the new accessory circuit didn't share anything at all with the existing system. No ground through the chassis etc. But separate ground wires to each component.
Or do you mean that the problem existed before?