Re: BIIIG OVERHEATING PROBLEM...small brake light problem...WTF!!!
Used bike? I'd change most of the fluids out as a start (radiator, brake, oil) and for sure check some of the longer items (like front forks). If your pump wasn't working, you'd know pretty quick - the engine would overheat much sooner. So, that's likely not the main issue..
I'd start with the radiator cap, and while you're at it, make sure the coolant is correct level inside the radiator by looking inside the radiator. If the cap is bad (which requires a pressure check), you might not have the reservoir working properly, and in addition, it can cause the boil over problem you're describing (it won't hold enough pressure to keep the boiling point higher). Then I'd move onto the water pump and the thermostat - at this point, you're into some major removal, so would make sense to check them both..
If you hear the fan kicking in, you know the fan and relay are good. Testing the temperature sender comes along after checking the pump and thermostat..