Hi!

The red light does go off, but only in "bake" or "broil", when the dialed
temp
has been reached. The light clicks on and off as usual during cooking.

But after shutting down the oven, and setting the dial to "OFF", the red
light comes back on as soon as the oven temp cools down to below the
thermostat

I have an old Hotpoint range (dual ovens, really big, old, but a wonderful
stove to cook on and very easily serviced) where the control for the primary
oven does this same thing from time to time. At first it worried me, but
after finding that the oven remained totally cool and that rotating the
selector knob through all the ranges would "clear" the light, I didn't worry
much about it.

http://greyghost.dyndns.org/stove.jpg (I haven't yet cleaned up tonight's
dinner!)

That has probably been five years ago. When switched from "bake" to "off"
the primary oven controller still leaves that red "bake" light on from time
to time. I'm not sure where the fault lies, and parts are still available
for my stove, but I see no point in replacing something that isn't really
broken.

I would guess that your oven experienced a more rapid version of the
"failure" that mine is experiencing when you shorted the element out.

If the red light eventually burns out, will it affect anything else ?

There should be no ill effect. My own oven's red light is still functional
despite having spent many days in the "illuminated" state. I doubt you will
miss it even if it does burn out and a replacement shouldn't be that hard to
find. I would assume that many different GE and other brand stoves use that
style of illuminator.

William