Flamethrower question

Hi, I have a really important tournament next week and wanted to ask a quick question, becouse im not really sure about the rules. In short im playing Germany and wanted to use the new Fallschirmpioneer squad (Cassino & Anzio) from "Italy: Tough Gut". Soldiers in this squad are all allowed to take pistols, even the flamethrower operator. So I wanted to know if I take a pistol on a flamethrower will he run away and be considered unarmed when he runs out of fuel? Or will he keep on fighting with only a pistol? I can't seem to find the answer anywhere. Would love to know what you all think : )