I had a quick look in my library and, below and hold, I can't find anything either
However, if you have a working example of both senders you can determine their characteristics fairly easily.
Set up a container with water in it over a hotplate, suspend the sender above the base of the container and connect an ohm meter to the sender terminals.
Like this but using the temperature sender: -
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Testing sender and thermostat.jpg [ 60.92 KiB | Viewed 4486 times ]
Heat the water and observe the resistance readings at various temperatures to produce something like this: -
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FJ20 temperature sender specs (Large).jpg [ 116.74 KiB | Viewed 4487 times ]
This graph is for the OEM sender as fitted to the FJ20 engine.
You can see that the sender resistance DECREASES and the water temperature INCREASES.
This is known as a Negative Temperature Coefficient device.
Once you have plotted the characteristics for each sender, you will be in a better position to ascertain what the problem is.
I'd be surprised if the senders exhibit major differences in readings, but because they are electrical, it doesn't take much to make the gauge readings meaningless
You may be able to add a trimmer resister to the circuit if the sender values are too low but let's wait and see what your results are first
If you decided to convert to a mechanical temperature gauge, all these problems will go away