What would Itlay have to do? - Brain dump time
I imagine that the Italian Fleet would have to sail to Valletta or even further afield and kept under the guns of the Med fleet (much like the HSF at the end of WW1) until a proper peace deal could be hammered out.
Who knows maybe those lovely Italian Fast BBs and Cruisers might see action in the Far East in 45 post a US refit as part of an Italian Contribution?
Italian formations in Russia would have to remain in place in the east - this is a difficult one - some how convincing the Russians to repatriate an Italian Army - maybe if it was kept secret enough the Italians minus their weapons could be repatriated via Iran? Perhaps the Russians could exploit the sudden holes opening in the lines etc but I suspect that the Germans would have gotten wind of what was happening and might interfere
German forces in Italy would have to be allowed to leave - again a difficult problem - I suspect this might lead to bloodshed anyway - Germany would then be obliged to leave forces in Austria and South Eastern France watching Italy
I can see the Allies possibly having to conduct an invasion of sorts if the Germans tried to take control in Italy during the confusion of the Armistice similar to OTL - but instead of an invasion to topple the government - one launched to save it - although after the Husky ops I suspect that more Germans would have been in country including some very powerful armoured units - and this would not be the case in TTL and an Italy intent on becoming a Neutral with fewer German forces in country might possible be able to pull it off.
Off course there were a fair amount of Italians who were just as Fascist as the Nazis. They would also be a problem.
I can imagine serious internal issues even if they did pull it off
Poor poor Italy
Mean while those forces that OTL invaded Sicily and Italy instead invade France.
Who knows after a successful invasion of France the Italians join the Allies - flush with US Built arms and open up a 3rd front with limited Allied involvement