65 Barracuda - Reverse light wiring "fix"

So my 65 Barracuda had reverse lights, originally. The previous owner installed a B&M Z Gate floor shifter and just left the reverse switch disconnected so the lamps have been dead for some time. Trying to revive them. That aside, wiring is pretty old and considering just running new wiring for this while I am at it. I am thinking to run a new hot, fusible link from battery to the reverse micro-switch on the Zgate and run a new line on the other side of it from the floor shifter over to the Driver's side kick panel and then connect up to the original wiring going from there back to the reverse lamps. Picture attached for what I am thinking but this way I won't have to get into the column and deal with old wiring to jump into. Anyone see any issues with doing this? That should allow the reverse lamps to function correctly when floor shifter goes into reverse the way its supposed to on the B&M Zgate...unless I am missing something...looking to FABO once again to ensure I am right..

reversewiring.png