Not sure how the bulb replacement could make the sound, but I suppose it is possible.
The two things that lead me away from the bulbs are the starting and stopping.
I may be way wrong, but are you sure it is not something to do with the rear suspension. I know you posted it as a 2014 RT, which should not have air ride on the back, but if it is an RTS or RT Limited, you get what could be termed as odd clicks and buzzes when stating out or stopping.
Again, likely wrong, but wanted to share that.
Editing on account of a quick check of your profile indicated it is an RTS, so maybe there is an unrelated leak in your rear suspension air ride, or possibly you made a setting change accidentally and the system is trying to keep up.