There was a confederate soldier in Virginia named Sigismund Zulavsky who has somewhere on the order of 50 record matches on FamilySearch, almost all of them based on images that are behind the paywall on fold3.com:
(The list also includes a few matches for a soldier in Connecticut, but that is a different, much younger man -- possibly the son of the guy in Virginia; more on that below.)
The only image that isn't paywalled is an index card; it seems to be a summary of Sigismund's military record, although I have no hope of deciphering all of the abbreviations.
Image, front: https://www.familysearch.org/ark:/61903/3:1:3QS7-89Z5-3YWC?i=2592&cc=2145147
(United States Confederate Officers Card Index, 1861-1865 - Wra-Zwi - image 2593 of 2602)
(ditto, image 2594 of 2602)
I'm trying to figure out whether this Confederate soldier could be Lajos Kossuth's brother-in-law Zsigmond Zsulavszky, husband of Lajos's sister Emilia.
Zsigmond, Emilia, and three of their sons arrived in the U.S. in the summer of 1852. Their fourth son, László, came a year later with his aunt Zsuzsanna (the youngest sister of Lajos and Emilia). From what I can tell, Zsigmond and Emilia's youngest, Zsigmond (1846-1863), rounded up his age by three years when he enlisted in Connecticut in 1861.
Based on their marriage record (Sátoraljaújhely, 16 Feb 1835), Emilia's husband was born about 1814 somewhere in Poland, and was Roman Catholic. (The Kossuth family was Lutheran.)
The sparse information in the fold.com indexes also gives a birthdate circa 1814 for the Confederate soldier (he's age 47 around 1861). For a birthplace, the reverse side of the index card says "Godova, Hungary". As far as I can tell, no such place has ever existed, but there is a Gdów, Poland, which in the 1800s was in Galicia, Austria, about 55 km (35 miles) north of the Kingdom of Hungary. (It's now about the same distance north of Slovakia.)
Do any of the images on fold3.com offer any more evidence?