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I've seen this issue pop up a few times here and have been dealing with it myself. Finally found a resolution that doesn't involve buying a new module or getting one from the junkyard with possibly bad bulbs.
The backlighting in my 2013 Express HVAC controls went dim, then died altogether. There are two bulbs, one died and the other followed. These bulbs are both made by JKL Components. They can be sourced though various electronics suppliers but MOQ applies and I wasn't going to buy 20-100 of each. Finally narrowed my search down and was able to find equal versions of each bulb. Just changed them out and everything is good. Total cost was $17 and took me 10 minutes to change the bulbs. Totally worth it to having working backlighting again.
Bulb 1 - Right side of controls, behind mode selector ****:
Specs (wattage/MSCP/lumens) are extremely close if not exact on both bulbs. The new bulbs are a bit smaller physically which is not an issue. Now installed, they match the rest of the interior backlighting.