First, ensure you have access to the Zendesk API. Log in to your Zendesk account and navigate to the Admin Center. Under the 'Channels' section, click on 'API' to ensure the API is enabled. Note down your subdomain, email, and API token, as you will need these for authentication.

Zendesk API requires basic authentication. Prepare your authentication credentials by combining your email (or username) with your API token. Concatenate them using a slash ("/") and encode them in base64. This will be used in the 'Authorization' header for API requests.

Determine which data you want to export, such as tickets, users, or organizations. Refer to the Zendesk API documentation for the correct endpoints and parameters needed to access the desired data. For example, to export tickets, you might use the endpoint `/api/v2/tickets.json`.

Use a tool like `curl` or a scripting language like Python to make HTTP GET requests to the appropriate Zendesk API endpoints. Ensure you include the correct headers, especially the 'Authorization' header with your encoded credentials. For example, a basic Python script using the `requests` library could be:
```python
import requests
import json
subdomain = "yoursubdomain"
email = "your_email/token"
api_token = "your_api_token"
url = f"https://{subdomain}.zendesk.com/api/v2/tickets.json"
response = requests.get(url, auth=(email, api_token))
data = response.json()
```

Once you have received a response from the Zendesk API, parse the JSON data. Ensure you check the response for status codes to handle any errors that might occur. If successful, extract the relevant data fields needed for your JSON export.

Organize the parsed data into a JSON format that suits your needs. If using Python, the `json` module can help serialize Python objects to JSON. Ensure the data is structured correctly, adhering to JSON syntax rules (key-value pairs, arrays, etc.).
```python
with open('zendesk_data.json', 'w') as json_file:
json.dump(data, json_file, indent=4)
```

Finally, save the JSON data to a local file. Specify the file path and ensure you have write permissions for that location. The above Python script demonstrates how to write the JSON data to a file named `zendesk_data.json`. Confirm that the data has been stored correctly by opening the file and reviewing the contents.
By following these steps, you can manually export data from Zendesk Support to a local JSON file without relying on third-party connectors.