Red to power and brown to ground , those are the heating element wires ! Put in an line fuse along the red line and a switch on the brown ground wire and it’s done !
You can buy the oem flex hose that goes between door and door pillar .
You could forgo the switch altogether and just leave the mirror heater on full time, as MB does. In my van the two heaters and the adjustment motors share the 10 amp Fuse #8, Fuse Block #2, so a 5 amp fuse will happily feed one mirror heater. Splice into a Start/Run powered circuit somewhere suitable under the dash and your mirror will stay warm and toasty all year 'round.
I'm still relatively new at navigating the Sprinter's wiring looms, so I will defer to wiser minds in selecting exactly where "somewhere suitable" should be, but...
Borrowing a few amps from the Wiper Motor relay's power supply line should be safe.
That's fed 20 amps via Fuse #6, Fuse Block #1, which emerges from the fuse module on Pin 2 of connector C3 as a Black/Violet 16 gauge wire. (see 8W-53 "Wipers" in the service manual).
Or you can tie directly into the fused Ignition Switch Run/Start output.
That's fed 30 amps via fuse #21, Fuse Block #1, emerging on Pin 4 of connector C2 as a Black 14 guage wire, and feeds several downstream circuits including Fuse #6 (see 8W-10-14 "Power Distribution").
Either of these appear safe tie-in points for a 5 amp fuse holder to feed your new mirror's heater, are close by the door hinge area, and would seem unlikely to cause side effects or overload any existing fuses.
Good luck,
-dave