Antifreeze in breather box 97 1300 yamaha tour deluxe

Is what the liquid plain water or coolant (water mixed with antifreeze). touch and smell the liquid, no smell = water, antifreeze smell and oily feel = coolant.
If plain water, could be Air Condition condensation dripping from condensation drain which is normal. (this drain is usually located near the center of the vehicle).
If coolant, could be leak(s) from: radiator, radiator hose, heater hose, water pump, engine freeze plug. A coolant system pressure test should show what is leaking.

If anti-freeze is actually coming out of the drain tube then yes, you could very well have a bad heater core. You may also be able to smell antifreeze while inside the vehicle if it is leaking. [Its a kind of sickly sweet smell] If just clear water is dripping out then this is most likely from normal condensation that is collecting and dripping off of the air conditioning evaporator core as the air conditioner runs. This condensation collects in the heater, a/c housing then drips out of the same little drain. Water from normal condensation will evaporate off of cement or pavement pretty quickly but antifreeze takes quite a while to evaporate away and feels slimy to the touch. It doesn't take much of an antifreeze leak before the cooling system gets low on so make sure you don't run low on coolant which can cause the engine to overheat.

you can take out the plugs - inject a little engine oil, crank the engine 5-6 times and reinstall, support the bike so the weight is off the tires, drain the gas and spray the tank with a rust preventative....