Hi LucasC,
welcome, I am not a mechanic but believe I understand the question, I'm sure much wiser better qualified people than I will pitch in but in the meantime
when you apply the right hand lever it is connected to a hydraulic system with a caliper at the wheel, think of the "click" as when the braking system begins to work
the left hand lever is connected to a drum brake on the rear (I think this is made of chewing gum and things from antiquity) so no "click" .
essentially the back brake is like an old fashioned bicycle where direct action of the cable relates to movement of the brake pads (shoes in this case)
this "click" should always be audible and unless you feel the clicking is excessively loud I would just enjoy your beautiful new bike man
