Why?

The "pop" most certainly is RF noise.  Here is what's happening.

The wire that is plugged into the stop light switch is too close to
the positive wire for the radio.  The "pop" that you hear is the
change in the electromagnetic field in the stop lamp circuit.

There are two solutions to the problem.

First and best is to find the circuit going to the stop lamp switch,
follow it up the harness and verify that it is located in the same
harness are the radio power wire.  If you find that to be true, moving
the stop lamp wire away from the radio circuit wire about a inch will
stop the pop you hear in the radio.

Second, if you can't locate the wire or find that the stop lamp
circuit is not in close proximity to the radio circuit, a Pi filter
should be installed in the positive wire leading to the radio.  A Pi
filter is the fancy name for an RF filter because the electronic
diagram resembles the math symbol for the constant Pi (3.1415926...).
Electronic symbol resembles this character (?).

The RF filter has an induction coil and a capacitor.  Without going
into details about how it works, the capacitor allows AC voltage to
pass to ground while blocking DC.  Thus, the errant AC (RF) current
passes harmlessly to ground thereby eliminating the pop before you
hear it in the speakers.

The Pi filter has THREE LEADS.  Two heavy leads (the input and output
positive leads) and one thinner lead which is attached to a ground.

Just follow the directions that comes with the filter and the "pop"
will be gone.  But first, try to find the wire and move it.  It's
known as induction since the AC magnetic field "induces" the current
into another adjacent circuit.

You can purchase a Pi (RF) filter at any radio shack (or at least
Radio Shack used to have them).

I hope this helps!