First, ensure you have the necessary Python packages installed to interact with both PyPI and S3. Use `pip` to install `boto3` for AWS S3 interaction and optionally `requests` to download files from PyPI if needed.
```bash
pip install boto3 requests
```

Set up your AWS credentials to allow your Python script to access your S3 bucket. You can do this by creating a file named `~/.aws/credentials` and adding your AWS access key ID and secret access key:
```ini
[default]
aws_access_key_id = YOUR_ACCESS_KEY
aws_secret_access_key = YOUR_SECRET_KEY
```
Alternatively, you can set environment variables `AWS_ACCESS_KEY_ID` and `AWS_SECRET_ACCESS_KEY` in your shell.

Determine the files you need to download from PyPI. You can either manually identify the package files or use the PyPI API to automate this process. For automation, you can fetch the package metadata using `requests`.
```python
import requests
package_name = 'example-package'
response = requests.get(f'https://pypi.org/pypi/{package_name}/json')
data = response.json()
urls = [release['url'] for release in data['releases'].values() for release in release]
```

With the URLs obtained from the previous step, download the package files to your local machine. Ensure you handle exceptions to manage any download failures.
```python
for url in urls:
response = requests.get(url)
with open(url.split('/')[-1], 'wb') as file:
file.write(response.content)
```

Initialize a Boto3 session to interact with your S3 bucket. Ensure you have set the correct region and bucket name.
```python
import boto3
s3 = boto3.client('s3', region_name='us-west-2')
bucket_name = 'your-s3-bucket-name'
```

Use the Boto3 client to upload the downloaded files to your specified S3 bucket. Loop through each file in your local directory and upload it to S3.
```python
import os
for file_name in os.listdir('.'):
if file_name.endswith('.whl') or file_name.endswith('.tar.gz'):
s3.upload_file(file_name, bucket_name, file_name)
```

Once the upload is complete, verify that all files are correctly uploaded to your S3 bucket. You can list the objects in your bucket using Boto3 to confirm.
```python
response = s3.list_objects_v2(Bucket=bucket_name)
for obj in response.get('Contents', []):
print(obj['Key'])
```
This step-by-step guide ensures you manually download package files from PyPI and upload them to Amazon S3 using Python scripts without relying on any third-party connectors or integrations.