Preferential Pronunciation?

It's short for Eterna.  It's not initials. So Eh-tah, Eh-tuh, or EE-tah...but not E.T.A.

oh, bonus, if anyone asks, it's deployant clasp, not deployment clasp 😂

While you are are spot on about deployant, but there is no official record as to what ETA stands for. What we now for for certain is Eterna had a subsidiary movement company called ETA,  but there are no records of why Eterna chose ETA as the name, why they used an acronym, or what that acronym could have represented. Many sources including ETA’s site at one point said it represents “Elegance, Technology, and Accuracy.” Googling that will find countless articles including many linkedin job profiles using that as the name for ETA. I am not as confident that is the case as it seems more like an afterthought slogan than anything else, but there is as much smoke around that than any other theory.

Short of someone unearthing long lost foundation documents, I am afraid this one is lost to history for us nerds to debate. 

Edit: From ETA’s corp profile page. Again, still feels more like marketing BS than actual history:

ETA SA Manufacture Horlogère Suisse
CH-2540 Grenchen
www.eta.ch
Elegance, Technology, Accuracy
Founded in 1793, ETA SA Manufacture Horlogère Suisse is one of the world's largest manufacturers of watches and movements. Backed by more than two centuries of specialist knowledge, ETA supplies watchmakers all around the globe.
All ETA mechanical and quartz movements are designed and built to the highest standards to deliver precision, reliability and performance. Among its many other achievements, ETA is noted for its historic role in the development of the SWATCH fashion watch, the enormously successful timepiece produced by ETA and first launched in November, 1982. Of particular interest today are the ETA competence centers, which supply ETA business units and third parties with specialist expertise in production technology and processes.
From research and development right through to ETA worldwide service, utmost care is taken with every quartz or mechanical movement to ensure outstanding quality. As a result, ETA is proud to supply the watchmaking world with products that embody three essential attributes: Elegance, Technology and Accuracy.

From a 2007 forum post directly from ETA (Swatch) in response to how to saw “ETA”:

Dear Sir

Thanks for your inquiry. How to pronounce is every one's personal opinion, it defers from one country to the other and also from one language to the other. So we leave it up to you how you pronounce our Company's name. Thanks for your understanding and best regards

Katharina Streit
Customer Counter
ETA SA Manufacture Horlogà ̈re Suisse A Company of The Swatch Group

I... use both. Even in my head when reading. 

I know that's maybe odd, but I do. I also would probably just mimic which ever way someone was saying it in person, were I to discuss such things in real life instead of just here on the interwebs.