I have confirmed with Blue Ox that their # BX3628 base plate kit for the 2014 Ford Taurus does indeed feature removable drawbars. This is shown in the installation instructions, I've provided a diagram from them showing the removable drawbars. Sorry about any confusion.
To complete your flat-towing setup, you'll need a tow bar like the Blue Ox Alpha, part # BX7380 which also includes safety cables. To wire your vehicle for flat towing, you can use a diode system like part # 154-792-118158.... view full answer...
The lighting coming from your RV isn't tied into the battery of your Taurus so it wouldn't have any effect, especially when using magnetic lights that would plug into the motorhome and be completely separate from the tail light wiring. If you're asking if you can use the Blue Ox Tow Bar Wiring Kit # BLU63FR that you were looking at then, no you can not because this kit is designed for specific Pontiac and Chevy models. You would have to use a splice in diode kit, like part # RM-15267, or... view full answer...