Hi comleyn,
this Italian peaked cap is ok, it's a M1934 of Artillery "Vice Lieutenant" and, as says Michael, is a variant on German style; the first version has a flattened top.
The name written inside "Unione Militare", was the largest producer of military clothing and had offices in major Italian cities.
The unit he belonged to the owner, is the 3rd Artillery Regiment "Fossalta", that belonged to 16th Infantry Division "Pistoia", it participated in many important battles, including the 2nd Battle of El Alamein.
It was deployed:
1940 France
1942 Greece
1942/43 North Africa, where it was destroyed by British Army and ceased to exist 13 May 1943.
Also the price seems me adequate.