Our 2008 RX350 had the same problem. The cover turned into sticky black goo that got all over your fingers if you used the outside switch. Apparently this is a problem several Toyota models are seeing too but no recall is in sight. I picked up a new switch at the Lexus Dealer in Scottsdale and they came down close to the internet price so for $60 I decided to get it over with. At first I thought about taking off the cover and sticking it on the old switch but it was such a sticky mess that I quickly gave up on that disaster. Come to find out it was really easy to replace, took maybe 30 minutes So here is a list of tools and steps you need to take
1. Buy Part. SWITCH ASSY, BACK 84840-21010
2. Tools #2 phillips and a 10mm nut driver that fits over long studs! or open end wrench will work too
3. open lift gate
4. gently pull on the lage plastic cover just below the rear window, (same one to replace tail light bulbs) it comes off pretty easy and the clips let loose with a firm tug. plus they are reuasable which is awesome!
5. Disconnect the light on the rear panel
6. using the 10mm wrench locate the 5 nuts on long studs that secure the bexel that contains the lift gate switch and remove them.
7. Gently pull the the rear bezel straight off
8. Note orientation of switch before removal to ensure proper installation of the new one. Facing rear of vehicle the wires should come out of the switch on the left side.
8. Unscrew the old switch and remove the two black plastic washers that are probably stuck to the switch.
9. Follow the wire from the switch, disconnect it on the inside and pop out the rubber grommet.
10. now put it all back together in revers order of these directions and you will be good to go!