Ok. It took me some time to look into this. But I can’t seem to find anything about the Pyreen alphabet in 2ed or 3rd ed.
The quote you provided is the entry for Jozhal in ToA. (3ed). the sentence preceding the quote you talks about “language composed of click, pops, and whistles.”. I did find a reference in 2ed of Pyreen speaking all languages of humans and demihumans. for 3rd edition in the Legends of Athas book you find Pyreen with the ability: Polyglot Pyreen can speak and understand any language. But I can find no information on what that alphabet might be or look like.
Knowing that Pyreen know all languages and that their alphabet may be used to represent the Jozhal language, you may want to turn to real world languages and writing systems for some inspiration. Take a look at the International Phonetic Alphabet (IPA) https://en.m.wikipedia.org/wiki/International_Phonetic_Alphabet
Which pretty much has a symbol for every sound one can make with their mouths to form words. The clicks may interest you. Which have also been used to represent thrikreen speech. Good luck.