It's at "THAT" point that I would just run a new wire from the switch to both of the red LED's in the back up light sockets. That would sure take less than 3-1/2 hours (But, yes, been there, done that in my own way).
BTW, how much brighter are they than just having an LED (white) in the red portion of the lens? My Protege (daily driver) has the tail/brake lights, center brake light and then I added a spoiler with a LED strip light (Red). So when I stop there are four distinct lights. But with today's distracted drivers it probably doesn't matter.
Side note: I had a 240Z years ago. I was under the dash one day and I found a socket with electric tape over the end. I though, that was odd. I pulled the tape to see the connector pattern, shrugged my shoulders and went back to what I was doing. Shortly thereafter I kept blowing fuses and couldn't figure out why. After HOURS of dealing with this it turns out that the socket I had found a few days before was for factory Fog Lights I didn't have installed. The electric tape was to keep it from dangling over a screw in the console that just barely contacted the inside of the socket. So, the tape that I didn't re-install..., did in fact have a purpose.
That only goes back to the saying of "What was the last thing you changed???"