I wouldn't recommend leaving the running lights active, first the tourpak already has running lights so you'll be making them brighter, second the difference between running and brake/turn is very close with the module, almost unnoticeable in the right light (as in daylight, not right turn signal light).
For the side markers, I've considered this, but that turns them off when the brakes are on also, not sure that is something I want to do. But I'm still undecided, if I did I would use relays and set it up so the brake lights line that I've disconnected in the tourpak is used on the other side of the relay to keep those lights on when the relay activates. So it would work like this.......
Right/Left turn signal.........relay goes from NC (normal closed) to AO (active open) turning sidemarker lights off when turn signal is on, and sidemarker lights on when turn signal is off, AO to NC (just as you describe)
Brake......relay goes from NC to AO but now there is power on the AO input also (from the brake light circuit in the tourpak) and sidemarker lights stay lit.
Just came up with this while replying, now that I look at it, I'm decided, I'm going to do this setup.......thanks for making me work thru it.....LOL