From atlaswealth.com: Australian citizens living overseas can vote in federal elections by registering as overseas electors under the Commonwealth Electoral Act 1918, allowing them to maintain their electoral rights for up to six years.
Voting does not automatically change tax residency status, but it may be considered among various factors by the ATO if residency is under review.
Expats should consult with a tax professional if their situation involves complex ties to Australia before casting their vote.