Have you tried replacing the LED driver board which is the power source for the LCD's backlight?
Here's the IFIXIT guide: [guide|1639|iMac Intel 27" EMC 2309 and 2374 LED Driver Board Replacement].
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=== Update ===
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Further investigating has pointed to a high current load of the LED strip within the display which burns out the LED driver board. This also can create a momentary flicker effect going off every 30 or so seconds.
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Sadly, both the display and the LED driver will need to be replaced to properly fix this.
Have you tried replacing the LED driver board which is the power source for the LCD's backlight?
Here's the IFIXIT guide: [guide|1639|iMac Intel 27" EMC 2309 and 2374 LED Driver Board Replacement].