It is not an uncommon problem. If you are lucky a squirt of something like Inox or CRC and using the switch will put it all right. Otherwise cleaning the switch is the next option, but watch out for all those small bits. The relay can go but much more rare. using Inox/CRC once a year on both switchblocks is probably good practice, as the kill switch can also play up after years of use and out in the weather.
Hard to remember, but many ST11s are at least 10 years old, often a lot more. I still have to get around the fact that I have a 1996 ST1100, and it is 17 years old. It still seems relevant and modern to me.