if the water keeps plankton away, then the light won't do any thing to attract them. being stained won't matter to plankton. i fish stained water and i find the plankton starting at 35 feet with a 50 foot bottom. if you have them, maybe find a deeper area and try to find them. turn your gain way up on your sonar. i'll post an image of what the look like on a digital sonar. also, if you can use an underwater camera, you'll see them at night because the light will draw them in like a bad fog.
we keep lights on top of the ice to share and to help bring in plankton on shallow water fishing. i use home made lighting. it's a day time driving light used for cars. i hot glued it to the side of an ammo box and have a sla battery inside and a switch on top. i can use to power led lighting in my shacks or use it by it's self sitting on ice helping us see and drawing in plankton.
i'd suggest looking else where to night fish if you can't find plankton.
the blue dashes are plankton. on flashers, they'll show up as low signal temporary lines. you can see them better on the left graph as blue lines, but you can them entirely. this is in the dark.

the yellow is bottom. the long blue line is my jig. the dash lines are plankton. the swoosh on my jig is a big crappie that was feeding and found my jig from above it. it came under it as they most always do and hit it from the underside.
no light needed to bring in plankton on this lake. you can see they come up to about 15 feet deep with a 23 foot bottom.
hopefully this helps and maybe you can compare it to where you fish if you can find waters like this.