It may happen for several reasons. Keep in mind that until the most recent LED display, the average Macintosh display had a CCFL lamp inside. Imagine a small neon tube. Well, on my trusty Macbook mine had lost quite its luster, before I got it fixed..
As you may know from visiting a local electrician, in time light tubes tend to lose a bit of their luster.
Furthermore, a dim backlight may be caused by the inverter, the small board that takes up some power from the logic board and pumps it in the CCFL lamp to make it bright and strong.
So, the culprit of a dim or absent backlight are usually:
1. An aging inverter board
2. A worn out power cable from logic board to inverter
3. An aging CCFL lamp in the display
As for your second question, according to iFixit all the G3 and G4 iBook had the same display
iBook G3 or G4 12" LCD Panel
So, yes, eventually you could swap them.
But if the backlight different is not that noticeable, I wouldn't try that.
Basically, you'd have to hack open your whole machine, and spend lots of time putting both of them back together.
You'd have to hack apart the display casing too, because the 1.33 had a different casing among all the other iBooks of the series, with the bluetooth antenna inside.
For an "aging" defect, it's not worth it. If I were you, I'd wait for the backlight to end its natural life before proceeding.