I just bought a 99 Limited and have yet to introduce myself, but this is one of the things I've had to fix since purchasing it.
In the service records from the previous owner, there's a complaint about this problem. SOUTH COAST TOYOTA of Costa Mesa, CA said the A/C control panel ass'y needed to be replaced for the tidy sum of $829.80. They wisely left it dark. What really irritates me is the Factory Service Manual instructs them to replace the bulbs before making that diagnosis. Crooks.
Truth is it likely only needs a couple bulbs.
You need a pair of each part numbers 81850-35020 and 81850-35030. One is for the LCD display and the other illuminates the buttons, but I can't remember which is which. I replaced all four.
The 99 dash couldn't be easier to get into.
Put one of those part numbers into google and you'll find a writeup. Like this:
http://yotatech.com/f5/part-ac-faceplate-bulb-40435/ They say the 020 part is for the LCD panel.