Just work out the vapor pressure
Above I've recycled an image from your other ammonia question, which tells more than you might realize.
Suppose your desert is a scorching 40 C. We look that up on this chart and it's maybe ... 16 atm. If your tidally locked planet has an atmosphere 16 times the pressure of Earth's, and there is a region over 40 C, it should be dry. At least, unless some perverse vagary of the world builder makes it lower than sea level - otherwise there could be a contest with inflowing ammonia, even a vast boiling planetary delta, but let's not get sidetracked.
The desert above isn't much like Earth's! On Earth we don't have a water atmosphere over water and dry land; we have an atmosphere with a slight amount of water over these. Our land is dry at far less than 100 C, and then we think a great deal about how dry. So how do we get there? Well, you'll need a second gas in your atmosphere. Nitrogen and hydrogen sound likely, though there are other possibilities. The point is, if your atmosphere is 100 times denser than Earth's, but only 16% is ammonia, then the ammonia will still boil away at 40 C. The vapor pressure of the liquid ammonia on the ground is the same, and if it's more than that in the atmosphere, it dries.
If that sounds like a lot of ammonia to have in the air for it to dry, well ... it is. If you look at water's diagram you see water starts off with a very steep curve, in log terms, so that the pressure at 373 K (1 atm = 101 J/L) is roughly 100 times greater than at 273 K. If we were using water at a high temperature near the critical point like ammonia, we'd have to have much more water vapor in the atmosphere to have an equilibrium of wet and dry.
Still, your planet can sustain wet and dry land. It can have deserts where the temperature is hot, or on high ground which reduces the vapor pressure of ammonia in the air and receives updrafts of expanding/cooling air from lower altitudes. (Frozen mountains are probably out of the picture, due to the red line on the left and the strong heat conduction of a thick atmosphere)