Start by logging into your YouTube account. Navigate to the YouTube Studio and access the Analytics section. YouTube Analytics provides a variety of data including views, watch time, audience demographics, and more.

In the YouTube Analytics dashboard, locate the "Advanced Mode" option, which offers more data insights. Use the "Export" button to download the data as a CSV file. This function is typically available under various tabs such as Overview, Reach, Engagement, and Audience.

Ensure you have Python installed on your system. Open your terminal or command prompt and install the `pandas` library, which will help in handling CSV data, and `json` for converting the data into JSON format. Use the command:
```
pip install pandas
```

Create a Python script to read the downloaded CSV file. Use the pandas library to load the CSV data into a DataFrame, which can be easily manipulated. Here’s a basic script snippet:
```python
import pandas as pd

# Replace 'yourfile.csv' with your downloaded CSV file's name
df = pd.read_csv('yourfile.csv')
```

Use pandas to convert the DataFrame into a JSON object. This can be done easily with the `to_json()` method. Specify the desired orientation (e.g., `records`) to format the JSON structure correctly:
```python
json_data = df.to_json(orient='records')
```

Write the JSON data to a local file. This can be done using Python’s built-in file handling capabilities. Here’s how you can save the JSON data:
```python
with open('youtube_data.json', 'w') as json_file:
json_file.write(json_data)
```

Finally, verify that the JSON file has been created and contains the expected data. You can open the `youtube_data.json` file using any text editor or a specific JSON viewer to ensure the data is structured correctly and matches the original CSV content.

By following these steps, you can successfully move data from YouTube Analytics to a local JSON file without the need for third-party connectors or integrations.