It sounds like a bad tail light, you should ask for a new one.
I'm not surprised, I had 2 of those tail lights back a couple of years ago.
They worked for a while (6 mo), then would not turn on any more.
I found I could swipe a magnet near the light and get it to turn on and off, and that worked for another 6 mo.
Finally, even that failed to turn it on anymore.
Since 2 lights failed for me, I switched to other 2W USB charged tail lights which are plenty bright.