Your Eagle has a/c heat pumps rather than electric heat strips. They give a modest amount of heat as long as the outside air is above about 45 degrees. It takes several minutes for warmish air to flow.
If the a/c provide does not heat, it could be that the reversing valve in the a/c is not working, but the odds that it failed in both a/c's is infinitesimal. A thermostat problem would be more likley.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC