Low Beams Don't Turn on. Is My Relay the Issue?

I have a 2003 Toyota Camry, and the low beams do not work. However, the high beams do work. This is my diagnosis.

1. I changed the low beam bulbs, and the low beams still don’t work.
2. I checked the 15A fuses for the low beams, and the fuses are not blown.
3. I checked the relay by removing the relay from the fuse box and provided ~7V to the “small” terminals. I heard a click and checked continuity on the “large” terminals. The relay appears to be working fine.
4. I checked the voltage at the bulb connectors when the low beams were on. There was no voltage drop. 0V on the multimeter.
5. I checked if the bulbs were properly grounded. They were properly grounded. Therefore, they are not getting power.
6. I checked the relay again by using the wand/stick that turns on the headlights. When I switch to low beams, I do not hear click. When I switch to high beams I hear a click.

7. I checked the wiring diagram for a 2003 Toyota Camry.
   

8. There is only one relay for both the high and low beams. Therefore, I think there should be a click for the low beams before the high beams. This does not happen.

My question is: is my relay the issue here? I would naturally assume the relay is the issue because it should click before the high beams are on. However, I got to thinking maybe it’s the wand/stick that controls when the high or low beams are on because the relay works properly when the high beams are on. Plus, I checked the relay externally, and it appears to be working fine. Any guidance is much appreciated.