Another possibility is this may be a visual symptom of failure
in the video analog board or other component that supports
the display. ~ Of course good parts are harder to locate.
Stuff with odd names such as flyback transformer, PAV,
and the like. And old sketchy solder joints to consider.
And may not be cost effective unless you locate extra iMacs
of similar vintage.... Then carefully don't electrocute yourself
in the process of learning how to trade parts between them
to rebuild the perfect beast.
Perhaps there is a reset procedure that may help see if the
display is really a problem; such as PRAM reset or a power
management reset. An original service manual may show
a hidden button on the logic board.
Several power-management reset methods were used among
different vintage Apple computers; a few are covered here
http://thexlab.com/faqs/resetpmchip.html (reset power chips)
but does not appear to have an easy keyboard shortcut for an
iMac G3. ~ Some had a reset button on the outside the case,
by the ports; others had one on the logic board by the battery.
So your quest to restore an early edition iMac G3 may be
fraught with mystery, intrigue, headache, & maybe shocks.
You may be able to locate an original PDF service manual.
To identify the exact build model can help locate the guide.
In any event...
Good luck & happy computing! 🙂