It's impossible to identify my nationalities - born in India but now simply an Overseas Citizen of India (OCI), Kiwi for 35 years, Aussie for 32 years. Although I'm a native Indian, I'm one of the paler ones with grey eyes, so I've had the confusion *in India* of being mistaken for a Westerner and offered to change money!
I have very little Indian left in my accent, but only well-travelled Americans pick that up. Aussies hear me as an Aussie and Kiwis likewise, as I didn't keep the Kiwi accent for long. I stick to the British/Indian/Kiwi versions of "dance/chance/advance", so in the UK I'm picked as a "maybe a posh Brit" or South African (never been there).
I have tried wearing a sober polo shirt with a small embroidered "Australia" on it, but unless you carry a stack of them, you can't wear the same one every day.

Tried a flag-motif cap once, but I'm not a cap person, so it didn't last more than one day. Yes, had the "Nous sommes Australiens, pas Anglais" experience in Marseille when a shopkeeper had no patience for our English. It didn't help that I learnt French in India from an Indian who hadn't heard native French. Hence I couldn't understand the gruff French in Marseille either.
So now I just have a discreet "Ansett Australia Frequent Flyer" and "Ansett Golden Wing" carry-on bag tags, which have been picked up by fellow Aussies.