Can you provide the name and the birth year? Anyone in the family could help with the birth place?
As he was injured there is a chance that his record still exist, but the search is very difficult with a common (frequent) name without other data.
Living in the Hungarian part of the Monarcy does not prove that he served in the Honvéd Army. I don't remember the exact ratio, but approximately 75% of the draftees were directed to the common (k.u.k.) Army and only 25% to the Honvéd Army (k.u. Landwehr).