so typically the way to identify the connector is by its pitch, then by pin diameter. That one is likely 0.1", 2mm or maybe something less common. You mention phone connector and looks like a coiled cord in the background so maybe the other end is a RJ9|10|22 handset jack? Typically the jack and wire is far more robust than the cord. Are you sure the clicker is bad and not the cord. Many time people try another cord and it does not work and assume its the device. Many non handset applications require actual wire in cord and lots of cheap handset cords are thin copper foil wound over string. Works fine for the extremely low current the mic and earphone need but not good enough for alternate applications people use handset cords for. If you just need to repunch what looks like a disconnected wire typically an ice pick or thin piece of sheet metal can put a wire back in place. It where you have to do a bunch that you need to find the right tool. Have several for different 0.1" and 0.156" pitch ones here, and you likely can buy on amazon or mouser.
