Thank you for asking this question
I have wondered the same in the past.
Before effecting a permanent fix by changing the fan clutch/fan on our 08 Journey with 350 Cummins 6.7L, I also experienced lights from overheating.
I never got to three different lights, however. It is my understanding that there is a sequence; 1st is high temperature warning, and 2nd is high temp STOP which throws a code. The first light alone does not leave a recordable code in the ECU. This is just my understanding, however, and may be incorrect.
As I moved uphill while driving, I could watch the temperatures rise. I understand that even as high as 210 degrees seems to me, that temperature is fine per Cummins. The light would come on at 215 degrees, and I pulled over.
At this point, I had the same questions as you, so I sort of split the difference. I was afraid to stop the engine completely and thus have no coolant flowing, so I allowed the engine to idle a few minutes. The light always went off after a short time - perhaps 90 seconds at idle. I then would shut the engine down after letting it run a bit more to cool off - which it always did while idling. I'm not sure if idling is the correct procedure, but I can say that the temperature always dropped consistently.
After walking the dogs or somesuch, I would crank the engine back up and proceed.
I did learn that if I geared down and let the engine run at 2100-2400 rpms (whatever gear was required to do this from 3rd or 4th), it would cool while running and I didn't have to stop etc., and the light wouldn't come on. The light typically came on when I didn't realize that we were heading up a grade or that cruise control was allowing the engine to lug and rpms to get down to 1500 or so (not an exact figure).
So - for future reference and barring something obvious like coolant spewing everywhere, in which case I would turn it off pronto....what IS the best practice?
Thank you for asking this question and helping my ongoing RV education. I'll keep an eye out for responses!
2008 Journey 39Z Cummins 350 ISB 6.7L
2006 Honda CR-V LX Tow