4th Brake light ?

[2008explorer4x4]

I installed one of those brake lights that fit in the trailer hitch. It was working correctly, I thought ? I was just told by someone following me, that the light works fine when I step on the brakes. When I put on the right signal light, the brake light blinks also, but only with the right signal, not the left ?
This was already prewired, I just plugged it into the small 4 way flat harness. Is the wire for the original 3rd brake light located some where near the rear tail lights ? Can I tap into this line ? not sure why the new one is not working correctly. Thanks for any help.

 

[Tech By Trade]

I had a hitch light that did the same thing. Its how they wired it. If you look the signal for the other side that doesn't blink is a blank. Saved big bucks on manufacturing not including that and I'm sure they passed them on to the buyer

 

[2008explorer4x4]

I decided that this light will not work properly as wired, there are only 4 wires on that flat plug and one is the ground. The others are left stop, right stop and running lights. There has to be a separate wire for that hitch light. I looked at the factory 3rd brake light top of rear lift gate. There is a purple/white wire that could be used, but it doesn't go to the tail lights. It goes forward under headliner. I could probably tap into that wire and try to run it down to the hitch light, but decided that it's not worth all that trouble, oh well live and learn.