Just to note, the standard 4-pin trailer wiring plug, does
not have a brake light pin/wire. If you connect up to the left tail light pin/wire, the "hitch cover light" will flash with your left turn signal. If you connect up to the right tail light pin/wire, the the "hitch cover light" will flash with your right turn signal. Sorry, but either way it looks rather dumb.
If you really want it to look and work right, you need to wire up something special (ie, non-trailer). One possibility is to connect up to the wire feeding the third brake light. I am not sure, but I think that the Message Center doesn't monitor third brake light's bulb(s). If so, you will not need a buffer module to isolate the "hitch cover light".