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You should try to "narrow it down" some. If the leak is the heater core, you can test by removing both hoses and plugging them. Then operate it some and see if the leak stops. As you said, it's best to be sure before dismantling since it's a big job.
I’ll run some stop leak through the radiator and see if that fixes the problems.
I could be wrong in my theory but I’m pretty sure that stop leak is bad stuff. Plugs up things like heater cores and rad cores. Use it if you have to to get home but otherwise I’d stay away from it. Just my opinion. Good luck.
Okay, now I do believe that is the condensation drip line
That is the evaporator condensation drain. If you have coolant dripping from it, the heater core is leaking. Its a pain to change, but could be alot worse. If you have ac , this is a good time to clean the box out, replace the blower motor if it shows and signs of needing replaced, and clean the fins on the evap really well.