Welcome.
You need to know the names for the components, so we can converse.
The "connect/disconnect" mechanism is called a hookswitch in non-Bell System language, and a switchhook in Bell language. On certain BSP's (Bell System Practices...the bible of the phone company) it is called a lineswitch.
The other parts are called the network (the thing with all the screws) the ringer, and the dial.
The gray-colored wire is not gray. It is "slate" abbreviated "SL" The abbreviation for gray would be GR which conflicts with GReen, so the color is called slate.
In most industry standard 2500 sets (i.e. those not made after 1990 and/or made in China) there is one extra lead from the switchhook that is not connected to anything. It is a transfer contact from the switchhook that is used for speakerphone service.
If you refer to this diagram,
2500D BSP you will see the SL lead is stored on terminal L2 of the network. Maybe that's where it goes in your phone.
