I have attached a section of the Militar-Schematimus for 1867 that gives some information on IR3. And I have translated a short section of Wrede's book that describes some actions of IR3 in 1859 and 1866. The war in 1866 was called the Seven Weeks War which Austria fought against Prussia and also Italy. Austria had over 500,000 men under arms in this war.
In 1859, in Italy, a battalion of the regiment fought at Sesia. The regiment fought, with distinction, at Montebello and then at the battle of Solferino. The 4th Battalion of the regiment was used against the volunteers of Garibaldi.
In 1866, the regiment was in the 10th Corps (Gablenz) in the northern army, the regiment fought at Trautenau, Neu-Rognitz und Königgrätz (Sadowa) with distinction, but with significant losses. The 4th Battalion was in Görzischen.