There are a fair number of texts in Carian in both southwestern Turkey and in Egypt, but archeologists had a devil of a time figuring out what they said. This was a bit odd, as the Carians used a variant of the Greek alphabet and, from what the archaeolinguists knew from non-Carian sources, the language wasn’t that unusual. Carian did have a bunch of additional symbols, but that wasn’t the biggest problem.
It wasn’t until the 1980s that John D. Ray finally cracked the code. His insight was that the Carian alphabet did not use the same pronunciation as the Greek alphabet! For example, a triangle was “l” and not “d” as in Greek. Gamma was “th” and not “g”.
Once they let go of the idea that the Carian glyphs had to be pronounced like the Greek letters, it was relatively straightforward to see Carian as a close descendent of Luwian. The presence of inscriptions in Egypt turns out to be due to a mobile labour force: Carians served as mercenaries for Egyptian rulers.
The Carians must have either forgotten about Luwian hieroglyphics or gotten bored with them.