Maybe I wasn't clear in the original post. My fault.
Our old thermostat was analog. It had a separate switch for fan operation (On and Auto) and another switch for Heat/Off/Cool, with a third switch to control fan speed (High and Low). The old thermostat had six wires going to it. Fan High, Fan Low, heat, cool, 12 volt hot, and a common. The new thermostat only has three wires, a common, a 12 volt+ and a 12 volt-. It is a Dometic (same at the A/C unit) and it is a digital with different Modes (Off, Fan, Cool, and Heat).
According to the operating instructions, once the Fan mode is selected, one can choose between High, Low, and Auto. When the fan mode is set to either High or Low, the fan is supposed to run continuously, no matter whether I choose Modes Cool or Heat. And that is where my problem lies. The fan shuts off with the compressor.
Everything on the new set-up is controlled through a controller box (new, with the new unit) mounted just below the A/C unit and accessible from inside the trailer. I have checked the wires and they seem to be hooked up correctly.
As for installing the old thermostat, it already got thrown out.
It is a single A/C unit, with a single zone thermostat.
Here is a link to the new thermostat
https://www.amazon.com/Dometic-3313192-000-White-Single-Thermostat/dp/B00C9OEZK6/ref=sr_1_1?s=automo...NWTraveler