We'll start with some preliminary observations. 1. The ethnonyms "Sik-ani" and "Sik-ouli" (or Sik-eli) is exactly the same name. Were they two separate peoples with the same ethnonym? This is a question posted today by all the historical scholarship and is notably pointed out by the eminent British Professor Robin Lane Fox. 2. This ethnonym is of Greek origin. It is etymologically derived from the name SIKELIA, which comes from the Greek «SKELIA» (SKELIA=Legs Skelos=leg) > (TRISKELIA = Three Legs - Tre Gambe in Italian). There is also the equally Greek name TRINAKRIA, from the "THREE AKRES" (THREE ENDS). The three capes: ΠΑΧΎΝΟΣ (Pachynos), ΕΛΩΡΟΣ (Heloros), and ΛΙΒΥΛΑΙΟΝ (Lilybaeon). 2.1. For these peoples (Sikani and Sikuli, or Sicani and Siculi) to be named with this Greek name, does it means they inherited it from some Greeks? A) Either they originate from a Greek region, as current historical research suggests is indeed the case. B) Or because the Greeks named them so, and consequently, we do not know the name by which they called themselves «in their own language». Sikeli and Sikani are, in any case, Greek ethnonyms. 2. They wrote using the Greek alphabet. However, the inscriptions that have survived are very few with a very limited vocabulary. They have not been understood. The biggest probability is that the languages are an older Pre-Greek, Pelasgian language, which has not been fully understood to this day. 3. However, the proper names, toponyms, and hydronyms are recognized as being the same, as those found in the region of the two shores of the Aegean Pelagos (Sea). 4. Regarding the Elymians, their Greek origin is much clearer.
SOTIRIOU et al. (Mon,) studied this question.