Yes, the 2000 to 2011 Rangers didn't have a "brake light" wire at the back, they have a Left turn/brake wire and a Right turn/brake wire, its called a 2 wire system
And no "green" brake light wires in 2010, that was on older Rangers
Dome light in a shell is more practical if it can be used without the key being on, but can also run down a battery if its left on, so there is a choice to make on that
You will need to run two 12volt wires to the cab, 18gauge, one for brake light and one for Dome light in any case, so use two different color wires
Each canopy bulb will have a Ground wire, they can be grounded at the frame in the rear
Canopy should have a Disconnect so you can just unplug the wires when canopy is removed, trailer connectors work fine for this
Brake light in 2010 Ranger uses a Purple/white stripe wire
Easiest access to the purple/white wire is at the Brake pedal switch under the dash
Unhook one battery cable, either one doesn't matter, do this any time you are working on electrical systems, even unplugging and plugging back in wires
Under the dash on the brake pedal assembly is a plunger type switch that activates brake lights, it will have a 4 wire connector, unplug it
You will see the purple/white wire, you need to Tap this wire, it will have 12v but only when brake lights are activated
I would use a 5amp inline fuse here, just in case, but up to you
If you want full time 12v for the Canopy dome light its also there at the brake pedal switch
There will be a Blue/red stripe wire on this connector, it has 12volts full time, again I would put another 5amp inline fuse on this wire
Canopy dome light would then have 12v all the time and you turn it on and off using its switch
You could install a switch in the cab to disable the 12v going to canopy dome light, if you are worried about leaving it on
Reason for the 5amp inline fuses is because these new added wires will not be as protected as factory wiring that is inside a harness
A short in one of the new wires would blow the 20amp brake light fuse in the cab fuse box, and you would lose all brake lights
If you add the 5amp fuses then just that fuse blows if there is a short on the new wires
If you want canopy dome light to come on anytime interior dome light comes on, i.e. like when you open a door, then there is "green"/blue stripe wire on the wiring harness for the fuse box in passenger side kick panel
Its on pin 8 of C2280C
In 2010 the interior light switch on the dash is a ground control, so not easy to use to activate canopy dome light, can be done, but you will need to add a relay