From what I have seen on this and a couple of other threads, the LS LED taillights use a series/parallel matrix, which means that if one LED dies, the others should keep working. You would need all of the LEDs in one row of the matrix to die to kill the whole array, but far more likely is that the current limiting resistor for that array goes high-resistance or open circuit.
In my experience the most common cause of LED matrix failures are the solder on one of the connections (on the limiting resistor, or one of the wires) so re-soldering the connections either end of your resistor may well fix the panel. They are also often controlled by relays, and those things are hopelessly unreliable compared to LEDs.
The LED itself will not break unless it somehow gets too much current and burns out. Even then only the weakest in the matrix will die until the array goes open circuit.

 

Agree and would add that using a resistor of a different tolerance and different shape than the old resistor would be perfectly fine, so long as you can solder the leads where they need to be.

Digikey has everything, even if you have to buy a pack of 50 resistors, what's that gonna cost, 5 dollars? One of you with a dead taillamp unit needs to crack it open and obtain the measurements of each electronic component. There's no way every single resistor, capacitor, inductor, etc failed, so you have a good chance of finding the spec for a good one.

If someone already replaced theirs and didn't throw out the dead one, or otherwise has a dead one sitting around doing nothing, feel free to postal mail it to me (PM for address) and I can try to identify the point of failure and how to get it working again. You'll have to cover shipping cost to me, and back to you if you want it back - this is purely a voluntary effort on my part as I don't even have LED tails on my LS, and it seems no one on these forums has identified what exactly failed in these taillights. My qualifications: Computer Engineer, provincially-licensed Professional Engineer (P.Eng), Senior Member of the IEEE (Institute of Electrical and Electronics Engineers). I also have electrical engineers on tap in the case that it is a particularly complex problem.

 

if anyone can identify which smaller resistors to purchase, please let me know. i have my2 inner tail light lens that i saved after purchasing replacements. mine are not completely dead. but there are several rows that are out. i was able to match the larger resistors and ordered them on ebay. but the smaller ones are what i'm having trouble finding.