You do not have to pull the radio all the way out to change the bulbs. You just need a small adjustable wrench, needle nose pliers and patience.
Use the Ford radio removal tool to pull out the manual climate control module a few inches.
Place the fan in the LOW position and carefully pull out the button.
Remove the electrical connector behind the fan switch.
The remove screw #1 with a small wrench.
Use needle nose pliers to twist and remove the bulb connector #2.
The other two bulbs are behind the paper #3.
A bulb is bad if the wire inside the bulb is broken. Find and replace the bulbs that do not work. You need to bring the bulbs with you in a plastic bag. Replace them with the same size, look and feel bulbs.
Here is how it looks after the bulbs are replaced.