There is a good chance you have a wiring issue or an issue in your fuse box.
Years back my FIL had a 2003 2500, 5.7, 4x4, quad cab short box. Bought the truck (used) to pull a fifth wheel, which it did okay but that 5.7 wanted to scream the hole time.
HOWEVER - our first trip out I followed him, and noticed that his left rear turn signal did not work. His brake light did but not his turn signal, though it worked fine on the truck. We confirmed the issue at the plug, all fuses looked okay, but there was an extra in-line fuse in an electrical tape wrapped harness that came out from under the fuse box (I have no pictures of this, it was a good 15 years ago). THIS fuse would show current when the left turn signal was on, but the fuse for the left turn signal in the fuse box did NOT.
At that point fixing it was beyond my skills at the time, so off to the dealer it went with the info we had. They kept it for a week until they discovered that it had essentially been re-wired to make the truck lights work, and there were two ways to fix it - put a whole new wiring harness in it, or put a Ford computer from a similar year in it.
The issue is that those year Rams had the turn signals using separate bulbs from the brake lights. This required the trailer harness (which uses the same wire for both lights) to be able to accept a signal from both of these separated circuits, and bypassing one on the truck means the trailer harness doesn't get the signal from it. Fords of those years, however, used the same bulb for turn signals and brake lights, so the electrical signal went through the same wire and fuse. By putting the Ford computer in it, the trailer harness would see proper signals, and the brake light and turn signal on the truck now used the same bulb.
I'm not 100% sure that this will solve your issue but it's definitely something to look into.