I mentioned this in another thread, not saying this is the cure, just my experience.
Bought a 2011 used with 75k miles. Center diff was never locked from previous owner, and work just fine for half a year, getting used a lot.
Switched the factory fill t-case fluid to a GL-5 75w-90 gear oil. Started getting these issues. Cold starts, the CDL would flash... and so on. Even going down the highway, CDL would start to flash.
Switched back to Toyota 75w LF. Issues stopped, and have not come back.
Oil background. Toyota 75wLF, we need to stop looking surface level at fluids, viscosity matters, but there’s so much more. Buy any 75w-whatever synthetic gear oil, it’s probably GL-5. That means it’s slippery. Like, that’s its main purpose, to be slippery, because it’s gear oil, you want that.
But our transfer cases (only mid 2010 and newer) started to require a low friction oil. Which is not slippery, but uses a much different molecular make up to reduce friction without being like KY jelly cranked to 11. In fact, a component requirement that wants a LF oil is a tell tale sign that slippery is going to hinder. Newer manual transmissions have already gone down this path, sure they used to require gear oil, but that’s not the case anymore. I believe the 200s newer t-case is the same way. Manufactures changed in mid 2010, and so did the oil requirement. But this isn’t like an engine going from 5w-30 to 0w-20, where they both require API SN oil, this is deeper. I think the slipper GL-5 gear oil is allowing something to slide into or out of lock, but the required LF oil that it’s designed for, is allowing something to stay put.
Do with that as you will, like I said, my problems with this was from a high quality synthetic GL-5 gear oil. Went back to Toyota’s 75w LF (low friction, not to be confused with their gear oil, which is names LT) and haven’t had another problem for 30,000 miles. Cold, hot, towing, rock crawling, and lots of highway.