The PDF you refered to does not have any one with a compatible pin configuration.
it's got 9pins, 5 on one side and 3 on the other, the middle on of the 3 is NC (Not Connected)
There might be a, or should be a working transformer out there, but as we have no specifications, it's a no go.
We can however measure them to some extent.
I would like to kill a myth right here thats been circulating for some years that the Game Gear uses the same transformer.
it's spot on, except for that gamegear uses yellow tape around it for isolation and TE/GT uses a red one, and it's the same
pin configuration the the same dimensions and the same pin pitch, so what to to, just now I unsoldered one on both a GG and GT
and started measure what I could, having no henry meter around me I used a single ohm meter just trying to see what pins
goes where and compare them, one pin didn't seem to be connected the same way, but one of the best ways to tell the difference
is between Pin 2 and Pin 9, the gamegear has 42 Ohms and the TE/GT 200 Ohms (ohm can be good for measuring coils and to some extent transformers too as it's a certain ohm per length, which means a certain amount of linings).
But hey I had to try it to, it could burn the transformer or another important component, but it's a spare unit with only the backlight working so..
Of coarse it didn't work, that we could already tell from the simple ohm difference, but it had to be tried, because if it would work (might be bad in long term though) a new supply of transformers would suddenly appear, and a lot of butchered gamagears...
Another myth is that you could use the GameGears light for the CCFL tube in the TE/GT and with this I think we can rule that out too,
not necessarily but highly probable as it should use another voltage (might be off with several hundred volts) and using another frequency.
I'm not saying it wont work but that it probably shouldn't, and if it did it could blow up in everything from a few seconds to a few days use.
So if just everyone out there would take their loose CCFL transformers with 9pins and get a 200 Ohm reading between pin 2 and 9 we might just
find the equivalent some day....
Now towards what you do have...
A transformer missing a leg
it might be fixable..
Probably it isn't rust you see, it's more likely the big electrolytes fluid that has eaten the leg a little (copper with tin on it and some lead), sometimes when fixing "GameGears" it's the fluid that has corroded the via holes, and measuring both sides of the via hole you will find the dead spot, it's an easy fix really, battery acid on GBA SP sometimes does the same thing, and battery and capacitors are cousins so, the electrolyte fluid eats threw iron, unplated copper, and even gold (I thought gold was so high up in the chain nothing eats on that except Chlore)
So the leg can be easily replaced but what about the little wire that was once attached there?
if that's ok there is a chance your transformer can be fixed...