Given your coordinates I would place you slightly North-West inside of Hamilton, Vic. You've stated Hamilton as your location though of course

54H is the zone (see the websites below)
0588610 is the Easting
5822687 is the Northing
The GPS has just added a 0 to the front of your Easting.
As for your Aus geod '66 and Aus geod '84 did you get them from your map or the GPS?
When inputing these settings under 'Position Format' choose 'UTM UPS'.
Under 'Map Datum' choose either 'Aus geod '66' or 'Aus geod '84'. Whichever is stated on your map book.
These are the menu setting names in my Etrex Legend (blue one). Not sure if they differ from the standard Etrex (yellow).
To get your position I used Oziexplorer and some maps I recently downloaded. They are Vic CFA maps. There are about 448 maps. When on the map sheet that incorporates Hamilton (map 431) it says for greater detail of Hamilton see map 431k on page 151. Is this the same map book you are using? These look to be very high quality scans of the book or perhaps they were digital to start with?
Have a look at these sites to get a better understanding of UTM.
http://www.dmap.co.uk/utmworld.htm
http://www.maptools.com/UsingUTM/UTMdetails.html
Bookmarks