OK, well if it dumped a pint or more on two different occasions, I would say two things: one is that the bike is now low on coolant (a quart is kind of a lot to lose) and the second is that something is significantly wrong. That is a LOT of coolant to lose, especially twice, and there is no scenario that I can think of that would explain it being normal in any way.
It could be something simple and easy such as a split tube or a tube that fell off a tank but frankly, the bike just should not spit out a pint or more of fluid- especially not twice without being refilled.
Very quick overview: when coolant is heated, it expands and so then of course, contracts when it cools. The highest point in any vehicle's cooling system should be the radiator cap, and so if the radiator (and entire cooling system of course) is filled right to the top then when the system is heated, there will be 'too much' coolant and it will overflow. In the olden' days, this would just spill out of the radiator's overflow tube onto the ground. Radiator caps have a vacuum vent so that when the system cools, they allow air to fill the radiator and cooling system to prevent a vacuum. After a couple of cold / hot / cold cycles, the radiator has purged all excess and the system should then run without purging any more fluid and yet be filled <pretty close> but not quite full to the top.
Modern systems add an overflow bottle or recovery tank (just different terms for the same thing) and capture that fluid that is purged from the radiator. There are now two hoses to the overflow tank: one comes from the radiator overflow and goes to the bottom of the overflow tank, and the other is a vent from the top of the overflow tank. When the system expands, coolant will flow from the radiator to the overflow tank but cannot leak out anywhere until and unless the overflow tank is completely full; otherwise, the level of the overflow tank just rises a bit. Then when the system cools down and a vacuum is created, the radiator cap applies this vacuum back to the overflow tank and draws some fluid back into the radiator. So, there is no normal circumstance where a coolant system will leak unless the coolant bottle is full.
I would suggest having someone (your or a competent mechanic as you wish) to look at the hoses on the bike, especially the one running from the radiator, just under the cap, to the overflow tank. Make sure it is not open or disconnected anywhere. The other thing that should be done is to find out which hose leaked in the first place and see where it connects. Finally, a good look over the whole system, including checking all components by using a vacuum gauge, should be done to see if there is any clearly failed part. Until those things are done there is really not much anyone can suggest as to what the cause might be, at least IMO. That said, as I said before, these bikes have proven to have very robust cooling systems as well as very reliable, robust engines so I would not assume anything really bad has happened- look for the simple, obvious things first and you will probably find a cheap and easy fix.
Best of luck.
Brian
Define puke: I would say a pint or two. It gushed out of the tube for about 30 sec or so.
Coolant has not been flushed.
I want to also note that we were at a high elevation (bluff at Perremarquette, Grafton, IL). Not sure if that makes a difference.
I am a bit confused with the overflow tank. Is the tank/reservoir that you can see antifreeze level? Or is it the small plastic bottle tucked away under the bike?