The shop manual for the Mark III is not very helpful when you try to change the transmission control selector indicator light...
I had no idea where to start so I contacted the excellent Lincolnforum where I got some very helpful tips.
2sasilverbullet sent me the following two pictures below to show what covers have to get removed to be able to access the indicator bulb.
You have to carefully remove these covers and you then get access to the bulb.
with the bulb already removed
The bulb is then inserted into the hole where you can see the finger.
After the bulb is replaced its pretty tricky to put the covers back into place. Be very careful to not break the plastic covers!