Have you got a picture of the switchgear? Might be able to find an alternative named/id'd part that's the same.
Alternatively, find any handlebar mounted button and wire it into the starter solenoid
(after checking that the starter solenoid is indeed working!). My dads bike (an antique from 1985) has been really difficult to start since he had it last year, new battery, wiring checked, etc. Turns out the starter solenoid was a pot of rust internally but looked pristine. New solenoid, starts first time every time!
https://www.aliexpress.com/item/32769288020.html This the one? There's two options A or B (looks like headlight switch or kill), £15 shipped. I'd always find a seller on Aliexpress that will take Paypal though as Aliexpress's "Buyer protection" leaves a lot to be desired.