After a search in two different directions, I found some information on what may be the correct VGA adapter for mirroring the internal display to an external; a page link and a product number. Appears to be obsoleted, but a call to Apple (main online store, or local Apple Store) should let you know if you'll be looking for used online, etc. Could be there is a new part number for this, or perhaps some authorized reseller has old stock? or a lucky find.
The adapter in question probably fit a few different models of that vintage, so someone online may have one if it truly is obsoleted. Some look similar but do not work the same.
•iMac G5 (iSight) Technical Specifications:
http://support.apple.com/kb/sp40
... and under Cables and Adapters:
Apple VGA Display Adapter M8639G/A
•iMac G5 (iSight) User's Guide (manual)
http://manuals.info.apple.com/en_US/iMacG5-iSight-Users_Guide.pdf
(Specs also lists Apple Video Adapter M9109G/A,
Apple FireWire Cable (4-pin to 6-pin) M8706G/A)
Hopefully this helps somewhat.
Good luck & happy computing! 🙂