Hi
It would be helpful to know their surname.
Switzerland is parted into 4 language region (italien, french, german and a part that has all of it roman). The first names of your grandfaher and is brother sounds like from the italian part (Ticino (i), Tessin (g)). This part is still pretty big to search for relatives with so little information but smaller than to seach for them in all Switzerland.
Have you asked at the imigration office in Australia? I could imagine that the had to register when they came to Austalia. Maybe you will find out where the said that they from. Good luck! Maybe you let me know some more information and I would appriciate to reseach a litte for you.
Regards,
Manuela from Switzerland