I googled "rv air conditioner wiring dometic" and found several Dometic manuals with wiring diagrams for various models. Each of these showed orange for a common lead to a thermostat.
On Colemans, orange goes to an overheat sensor (bimetal thermostat) that opens when the heater gets too hot. But you said yours is Dometic.
You can probably download the installation manuals for your particular equipment from Dometic. Your photo isn't clear enough to read the wiring diagram on the label.
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-- Carl
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