How do I back up my iPad on my external drive?

Apple does not allow for back up to an external hard drive. There are three methods of backing up your iPad. Two do not use iCloud. You can read about them here:

How to back up your iPhone, iPad, and iPod touch - Apple Support

This support page outlines the natively supported backup methods for iPad and iPhone:

How to back up your iPhone, iPad, and iPod touch - Apple Support

Native iOS/iPadOS backup and restore processes are dependent upon iCloud, or connection to either Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS).

Natively supported methods offer full system backup - consisting of data and device settings.

How to back up your iPhone, iPad, and iPod touch - Apple Support

It is possible to use a third-party App to backup data (but not device settings) to a variety of external storage options - including third-party Cloud services, external media devices and network storage. One App that comes readily to mind is FileBrowser Professional by Stratospherix:

https://apps.apple.com/gb/app/filebrowser-professional/id854618029

You would be well advised to review the extensive online Manual and help files to determine suitability for your needs.

https://www.stratospherix.com/products/filebrowserprofessional/filebrowser-professional-user-guide.php

FileBrowser also integrates with the native Files App, further simplifying file/photo management. There is a learning curve, but it works.