I would suggest adding a Shared Parameter for each connector element you have labeled Connector Description #N incremented or named based on your needs.
Then associate those parameters to the Connector Description parameter of each connector within the family editor.
Add the shared parameter to your Revit model and apply it to the family types required.
Schedule the elements you require and ensure the new shared parameters are columns in your schedule.
Export the schedule to Excel using the Revit exporter or preferably the DiRoots Sheet Link app.