I have a single pole switch that controls an outdoor light. There are no other switches controlling the light. My switch, though, has four wires plus the ground (see attached photo). Two of the wires are screwed in on the side, while 2 are inserted in the back. I'm lost on how to hook up the Caseta Wireless switch in place of this switch. The only thing I can think of is that an outdoor receptacle could be drawing power from the switch/wires. Any help is greatly appreciated.
Like you said, most likely the second set of wires runs to a plug and the switch controls power to both. I take it that you can verify if the switch controls power to a plug. If so, and you only want the Caseta for the light, obviously you will have to isolate the plug by removing it from the light switch and pigtail the line wire to feed power to the plug separately from the switch. I am not an electrician--just my 2 cents.
Okay, here's what to do. You have two black/white pairs. One is the power feed and one is the switch loop. If you remember your past experiments, you already know which is which. Otherwise you can repeat the first two experiments you did to find out. Do not repeat the experiment tried by your bonehead friend!
The power feed is the black/white pair that makes the light on all the time. The switch loop is the black/white pair that makes the light not work at all. So, now
Connect the black wire of the power feed to the white wire of the switch loop. Neither of these wires connect to the fixture.
Connect the black from your fixture to the black from the switch loop.
Connect the white from your fixture to the white from the power feed.
Connect all grounding wires.
That's it. It'll work. I guarantee it.
When you go to turn the breaker back on, be sure to push it all the way to off, and then to on. You may also have a GFCI that needs to be reset.
The wire inserted in the back and the screw terminal are connected inside the switch. Instead of twisting the wires together and adding a pig-tail, they made the connection on the device. This is a very common technique. There are a number of reasons why they would run 2 wires to the lights (switch-leg). Just keep the wires paired the way they are and you will be fine.