I have a 2001 Sonata and both the brake and charging light turn on and
off together intermittently (every few minutes). When it happens I hear
a small click (almost like a turning signal sound, but only once and
much fainter).

Also, if I do actually turn the parking brake on, the light becomes
brighter. So I am guessing it is not an actual parking brake problem.

Does anybody know what it could be? And is it serious?