While often mistaken for Australian, the GEICO gecko's accent is British. More precisely, southeast English (London or home counties). The British/Australian mix-up is used to comic effect in a...
It does not have either of those accents. In one of the latest commercials he says he isn't British or Australian. I was searching and i found out he has a New Zealand accent.
If you are trying to find out the name of the song that plays at the appearance of that silly prop (a stack of money with the eyeballs on it), then the answer is that it sounds like a remake of...