That CAT grid heater really sucks the juice. Check your batts while somebody turns the key on and you will see the big drop, keep your leads on the batt and see if the volts come back up after about a minute. You show 12.59V which is basically a full charge I wonder if you have the coach plugged in and are getting just a surface "full" charge which is getting killed by the grid heater, then you are below 10v or so and that is preventing a neutral signal and keeping you from a start???
You might pull batts and have them load tested or if comfortable with big amps jump your starter and see if the CAT will turn over. Check batt connections and clean batt and chassis grounds CAT's are serious about clean power, at least mine was. And remember volts are not the same thing as amps a surface charge might look good, but a bad batt, low amps no muscle will just not do the job.