The Sun's hour angle, measured around the celestial equator, changes at a nearly constant rate.
The gnomon of a sundial is aligned with the polar axis to take advantage of this.
The celestial equator is oblique to the horizon except at the Earth's equator and poles.
The lines of azimuth converge at the observer's zenith and nadir, so the Sun's azimuth changes more rapidly near one of those points (e.g. summer midday, winter midnight) and more slowly near the horizon.
The amplitude of this fluctuation depends on the Sun's declination and the observer's geographic latitude.
For an observer in the tropics, on a day when the Sun passes directly overhead, its azimuth swings abruptly from 90° to 270° at noon.
For an observer near the north or south pole, the Sun remains near the same altitude all day, and its azimuth rate stays near the average 15°/hour.