To begin, you must access the Google Search Console API. First, navigate to the [Google Developer Console](https://console.developers.google.com/), create a new project, and enable the Google Search Console API. This allows your application to interact directly with the Search Console data.

After enabling the API, you need to set up OAuth 2.0 credentials for authentication. Go to the "Credentials" page in your Google Developer Console project, click "Create credentials," and choose "OAuth 2.0 Client IDs." Configure the consent screen, then download the generated `credentials.json` file, which will be used to authenticate API requests.

To work with the Google Search Console API in Python, you need to install some libraries. Use pip to install `google-auth`, `google-auth-oauthlib`, and `google-auth-httplib2` by running:
```bash
pip install google-auth google-auth-oauthlib google-auth-httplib2
```
These libraries handle authentication and API requests.

In your Python script, set up the authentication flow to access the API. Use the credentials file you downloaded earlier. Here’s a simple example:
```python
from google.oauth2 import service_account
from googleapiclient.discovery import build

# Load the credentials
credentials = service_account.Credentials.from_service_account_file(
'path/to/credentials.json',
scopes=['https://www.googleapis.com/auth/webmasters.readonly']
)

# Build the service
service = build('webmasters', 'v3', credentials=credentials)
```
Replace `'path/to/credentials.json'` with the path to your downloaded credentials file.

Use the API service to query the desired data from Google Search Console. You can specify the site URL and desired metrics, such as clicks, impressions, etc. For example:
```python
request = {
'startDate': '2023-01-01',
'endDate': '2023-01-31',
'dimensions': ['query'],
'rowLimit': 1000
}

response = service.searchanalytics().query(siteUrl='https://yourwebsite.com', body=request).execute()
```

Once you receive the response, you need to process the data. The API response is typically in a dictionary format, which can be directly manipulated in Python. Extract the necessary information using:
```python
data = response.get('rows', [])
```

Convert the processed data into a JSON format and write it to a file. Use Python's built-in `json` library:
```python
import json

# Convert data to JSON and write to file
with open('search_console_data.json', 'w') as json_file:
json.dump(data, json_file, indent=4)
```
This writes the extracted Search Console data to a file named `search_console_data.json` in a readable JSON format.

By following these steps, you can effectively move data from Google Search Console to a JSON file without the need for any third-party connectors or integrations.