My son recently got 2 strip lights for his Traxxas 4 tec 2.0 (T-Bone Racing Rocklight Underglow LED Strips). Our plan was to run them off the third channel of the receiver, so I soldered the two strips together and soldered a receiver plug on to them. When I connect the receiver plug to a female plug connected to an alkaline 9v, the strips light up, but when I connect the plug to the 3rd channel on the receiver, nothing happens. I thought the third channel on the receiver was supposed to be always on.
What am I doing wrong?

There should be power ( 5 to 6 volts ) at the reciever .
Red/Orange = + Power - middle wire
Black/Brown = - Power/Ground
White/Yellow = Signal wire ( dont use this one )

That's how it's all wired. Is it possible that the 5-6 volts isn't enough to power the lights?

yes.
another thing you could try, solder jumper wires off the ESC battery connector. that will wire the lights directly to the battery and give you 7.4 volts (based on a 2s lipo). see if that works.