In the manual:
To save battery consumption, the meter may be turned off by sliding the switch to the OFF position immediately after you have made your reading.
If it wont switch off, then obviously the switch is defective. The finder needs to be disassembled to expose the switch so that it can be diagnosed and fixed or replaced if necessary.
Unless you feel competent to do the job, the finder will likely have to be sent to a camera repair shop for repair. A high-volume camera repair business is likely to have technicians that have seen this before, know how to deal with it, and know where to obtain replacement parts if needed.