Super nice engine, they used that same engine in an Arctic Cat Lynx snowmobile. Very under stressed in the TS250 chassis. The models electrics were virtually unchanged for many years so an older schematic should be goodbut don't go crazy with power consumption or fancy batteries and lights or you will have problems, the regulator is just a big zener diode. If you can't source electronic parts for the TS250 try TS185 parts, many are directly interchangeable.
If the horn is rusted replace it, they rust out and short out when they are very old, the horn is one of the highest power draw items on the 6 volt system, and the engine does not require battery power to operate.
Well first off you are in luck because LED is low voltage, you don't need 12 volts to run LED devices.Thanks for the info. I was thinking of changing the lighting system to a 12v system so I can run a led headlight and taillight otherwise I think a horn is the only other thing I will be running on the electrical system. Someone else already stripped all the signals and everything so it will be almost a complete rewire.
Well first off you are in luck because LED is low voltage, you don't need 12 volts to run LED devices.
Cheapest easiest way to put lights on that other then stock original would be a dead loss battery system, absolutely nothing on that motorcycles electrics are compatible with modern solid state batteries or auto LED lighting devices. Run dead-loss and plug it in to charge when you're not using it, just like we will be doing once all of our vehicles go electric some day.
If you do rewire, definitely upgrade the fuses to automotive blade fuses, and incorporate separate circuits for major subsystems.
Additionally, spend the money on good quality crimp connectors, crimpers, heat shrink, and fabric wire tape.