Where's the fuse located for the third brake light on a Ford 2003 Taurus

Passengers compartment fuse panel (fuse #17) This is your stop lamp fuse. If the third brake light is out, i'd check the bulb (if not led) but it's most likely the brake switch. Hope this helps.

Is there a separate switch the third brake light separate from the other two brake lights?

It has no bulb on the 03, it's led. To replace: kneel in backseat, facing rear glass. With both hands pull the stoplight housing towards you about an inch, then angle the rear edge up while you pull, and it will come out of its slots in the rear shelf. Only pull it back about 4", just enough to allow access to to the small wire harness and plug. Pull slowly and carefully on both sides of the plug to separate, not on the wires! Flip the LED housing over, and note the LED banks orientation in the locking tabs. Make sure you have a replacement bank ready to install (ebay, OEM part from dealer, or self-pulled from a salvage yard, as mine was) while you do this. Starting at the wires harness side, carefully pull the locking tab open just enough to lift one side of the LED strip out of the housing (careful of the locking tabs), and continue to lift at an angle until it comes free. Place the replacement part (in the same orientation the original was in) on top of the locking tabs/slots, and press straight down gently, untill it slides/locks in to all the tabs/slots and is fully and correctly seated in the housing. Set the unit upside-down (red lens facing front of car) on the rear shelf, and reconnect the plug, it only goes one way. Move to driver's seat, and press the brakes while looking in your rearview mirror at the lens, it should be working. If it is, return to back seat, flip the housing over with lens towards the glass. Carefully feed the wiring harness back into its hole, as you angle the housing slightly, and slip the housings bottom tabs into the slots in the rear shelf. slide it towards the glass untill the housing drops down flush with the shelf,and continue to slide it rearward about an inch, until it locks in place on both sides. You're done. If you get yours at a salvage yard, be mindful that most require you to buy it as a unit, instead of just the LEDs. It's still cheaper than just the new LEDs at most places. My unit (2000-2005 Taurus) cost $6.00, and was pulled from an 02 Taurus with different color interior, and was switched out in the parking lot in about 5 minutes.