Hi Sinclair,
Guess you're right, have a Sammy UE40J5100AK where those little Leds keep popping off even before they turn Blue. Changed a couple, and set back in a month with more gone. Thought to reassemble, then found four more flickering using the tester.
Note Ebay does 100 x A137CECEBP18A for a Tenner, and they look like the originals, so you could sort a couple of pretty big screens or several smaller ones with a hot iron in each hand.
Trying suss something, where with small spots of solder paste, can sort soldering, heating the back of the strip. First try, used too much paste and the Led popped off somewhere, never to be seen again. Now sorted a bit of aluminium channel, a metal clad 3R3 50 watt power resistor and a 250C cut-out - Might work with a 12v 4a supply, or not.