Since your external hard drive still keeps disconnecting after trying out multiple methods, the only resort for you now is to update or downgrade the current macOS. Hopefully, you can fix external hard drive keeps disconnecting Mac.
How to update macOS:
Step 1. Click on the Apple menu from the top-left corner. In the drop-down list, choose System Preferences.
Step 2. In the Apple setting panel, find and open Software Update.
Step 3. It will check for updates by default. If there's a macOS update available, click on Upgrade Now to update your macOS to the latest version.
Your Mac will restart when the upgrade is finished. Try connecting the external hard drive to it now, is the drive still disconnecting off and on?
How to downgrade macOS:
Unlike macOS updates, downgrading the macOS will erase every piece of data on your Mac device. Therefore, backing up the system is a must-have. You can either back up the Mac by using the Time Machine or other cloud storage methods. After that, follow the simple guide below to downgrade the OS.
Step 1. Spare enough space for the older macOS by erasing your Mac hard drive in macOS Recovery mode. Otherwise, you'll face dilemmas such as macOS downgrade failure or slow performance.
Step 2. If you've backed up the system with Time Machine before upgrading to the current system, you can easily downgrade macOS by choosing the backup file in the Restore from Time Machine Backup option.
If you don't have a Time Machine backup, you can downgrade the system by choosing the Reinstall macOS option in macOS Recovery mode.
Moreover, you can downgrade macOS by creating a bootable installer. Ideally, you should fix the external hard drive keeps disconnecting on Mac issue with a correct OS running.