I have an almost identical box on my eBike. And I have a LED taillight built into the reflector area as well.
Look to the right. There's the "touring kit" which I have. The box looks pretty much exactly like yours.
All I did is take an off the shelf rear taillight with 2 LEDs. I disassembled it and mounted it to the inside of the box with the LEDs poking through holes behind the lens. The switch is on the inside of the box, which I don't mind.
It works perfect.
I'll take pictures of the box and my mods if you want.