For some people, the jarring motion of brisk walking can produce what is called a seismic effect which causes movement in the small bones or contractions in the muscles of the middle ear space. You can experiment to find out if this is the cause by walking slowly and smoothly to see if the clicking is present. Then, try walking quickly and with a lot of motion to see if you hear the clicking. You can also test for the seismic effect by moving your head up and down quickly.
A common cause of tinnitus is inner ear hair cell damage. Tiny, delicate hairs in your inner ear move in relation to the pressure of sound waves. This triggers cells to release an electrical signal through a nerve from your ear (auditory nerve) to your brain. Your brain interprets these signals as sound. If the hairs inside your inner ear are bent or broken, they can "leak" random electrical impulses to your brain, causing tinnitus.