I just did this on a '66 250S. This will be a good test of your toolkit versatility and manual dexterity in confined spaces.
First disconnect the battery. On the W108 250S, the whole instrument cluster comes out, but on the W111 coupe, I believe just the speedometer needs to be removed. From under the dash, you may need to reach up and remove a knurled plastic or aluminum thumb-nut to release the speedometer. Then it should clear the dash far enough to be able to unscrew the speedometer cable. Through the dash-hole vacated by the speedometer, you'll need to use a stubby or offset screwdriver to remove the 3 slotted screws that hold the ignition switch to the back of the steering lock. Once the switch is free of the lock, you can manouever the switch in the hole to remove the 5 philips screws and release the wiring. It may be best to release and transfer each connection to the new switch, one at a time, to avoid mixups. During installation, make sure the new switch body aligns with the lock housing and the rotating switch center aligns with the cylinder drive pin. Reconnect the battery and check that the switch functions properly BEFORE you reinstall the speedometer.

Happy Motoring, Mark

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DrDKW