I've sure no definitive answer, several possibilities do come to mind, all may be hooey.
I'm liking mackguyver's suggestion that it might be vignetting, I think that would be easy to test.
With the same set up, change out the circuit board as subject with plain paper as subject, if lens/extension tube vignetting is the issue it should be readily apparent.
I'm thinking this one is way off the wall, but I'm thinking it anyway.
Wondering if light is reflecting off the solder pads, maybe bouncing around between the pads and the lens.
Try shifting the part that now shows brighter off to one side of the frame. If that part remains brighter, it's a light distribution issue, see Jim Saunders' radial filter in LR suggested fix.
Is it possible in your set up that light is coming through from the other side of the circuit board? If so, that should be easy to block. The central, green part of the board might well be able to pass light that would be blocked by the adjacent IC chips.
And, it's quite possible that the answer you seek is something else entirely, I freely admit I'm only guessing.
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