The law in Italy is that you must wear a helmet if the 3 wheeler does not have a roof or a "survival cage" (that would mean that your head could not hit the ground in a roll over. It is just possible that the higher roll bars specified for Australia may meet the requirements but the current roll bars certainly do not. Further more if seatbelts are supplied you must wear them. The Ape has a roof and that is why a helmet is not mandatory. Some of the newer ones also have a robust external roll cage. Helmets must be worn in the 3 wheeler trucks without a roof and the police are well aware of this.
There are no ifs and buts about this and it is official that you must wear a helmet and seatbelts in a Morgan 3 wheeler in Italy. You must also have a motorcycle licence, ridiculous as it may seem. If you do not comply with these laws you risk a big fine and having the vehicle sequestered.
Having said that I believe most police and carabinieri would be somewhat ignorant of this and/or perhaps not bother a tourist so you may get away with it, as many have done. The risk however is there and you only need to get pulled up by someone who is stroppy or dislikes tourists and it could really ruin your holiday. The choice as to whether to take the risk or not is up to you.
By the way those scooterists down south risk it as well. A few years back one refused to stop at a roadblock when he was being pulled up for the umpteenth time for not wearing a helmet. Apparently the safety was not on on the officers machine pistol so that when he jumped back out of the way a burst went off. Oops! Our apologies to the widow.
In that case a four wheel Morgan also need to wear a helmet ??
It has no roof and no roll bars.