https://www.holdenmorgan.co.uk/parts/Classic_2014_v5.8_.pdfThe above link is to a Morgan parts book via Wolf performance website links page - its a huge pdf file that takes an age to load - but should help you locate a new switch if needed. Have you tried pressing it on/off a number of times? may help if its a dirty contact for example.
I think the fog light circuit may well have its own fuse too - worth checking first
on my car it works with dip and main beam.
The part number is ( Morgan) MDE15270 ( fog light switch). I would imagine any helpful Morgan dealer would be able to order one.