Here's a post that will give you the information you need to determine if the leak is coming from the water pump seals (not good) or from the V in the middle of the engine (also not very good, but somewhat less critical and generally easier to fix):
ST1300 - Water Pump Weep Holes
Be aware that if you wash your motorcycle and you do a really good job of washing it (spraying water from the garden hose everywhere, especially into the sides of the engine), some of that wash water will accumulate in the V between the cylinder banks and just sit there. Later, if you start the bike up and move it around, that water will then run out of the square hole. That's normal, nothing to worry about - in fact, that's why the square hole is there, to let liquid trapped in the V of the engine drain out. From what you wrote in your first post, I think that is what is happening to you.
If you have small leaks (insignificant leaks) from the various hoses in the V of the engine, the leaking coolant residue will get washed out with the water you used to clean the moto. This might cause you some worry because it will look like coolant. What you need to do is determine what the rate of coolant loss is.
Keep track of the coolant level in the reservoir bottle on the left side of the engine, down by your left ankle. If it only goes down a little bit over the course of a riding season (for example, you lose an inch of coolant over 6 months), it might not be worth your while to start tearing the bike apart to find the leak. On the other hand, if you are losing an inch of coolant once a month, it might be appropriate to find and correct the problem.
l see from your profile that your bike is a 2007. That means that the coolant hoses are now about 14 years old. If you plan to keep the motorcycle, it would be prudent to plan to replace the hoses & clamps within the V area next winter. I understand that Wisconsin winters are long enough to let you get the job done at a leisurely pace...
Michael
