The book "Conscripted Slaves: Hungarian Jewish Forced Laborers on the Eastern Front during the Second World War", by Robert Rozett, has information about overall conditions and experiences of the people in the labor battalions. In the index specific KMSZ units are mentioned, and there is a brief mention of 105/32. It basically matches your information, in that it states "on July 2[5]th 1944. ... 120 men from the 105/32 KMSZ Company in Krasnoye ... went missing."

You should try contacting the Hungarian military records archive at  hadtortenelmi.leveltar@... -- give them everything you know (father's name(s), date and place of birth, unit number, etc.) When I have enquired I have received an answer in about a week. They were able to locate a small amount of additional details from military records and also from some historical works on the Labor Batallions (a documentary book by Elek Karsai, „Fegyvertelen álltak az aknamezőkön…” ("They stood unarmed in the minefields...").
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Peter Cherna, Exton PA (peter@...)
Researching CSERNA (Budapest, Székesfehérvár), GRUNFELD (Székesfehérvár), BRAUN, REINER (Budapest, Nyíregyháza, Máriapócs), EHRENFELD (Pozsony, Balassagyarmat) BRACK (Ipolykeszi)