Mine came with a digital control that let's me adjust whether or not the fan is always on. (But then, mine said it would come with a Dometic, has the paperwork for a Dometic, but actually has a GE, so go figure.) Anyway, if your control doesn't let you specify whether the fan is on all the time or auto, you should be able to replace it with one that does. This is usually very easy to do.
A possible option (if yours controls both AC and furnace):
https://smile.amazon.com/gp/product/B01M8LFHT3
Note the "Fan Mode" switch. That controls whether the fan is always on ("On") vs. turns on and off as needed ("Auto").
There are similar ones for just AC.