How can I get to recovery mode for IMac when using external screen

I don’t think Recovery supports that.

Use Target Disk Mode and use a cable and another Mac to get a backup, if that’s where this is headed.

Alternatively, install macOS on a bootable device, and (try to) boot that, on the off chance the storage has failed.

Or get the iMac repaired.

You can try pressing Command + F1 to see if it will enable mirroring mode. If the keyboard has the "Fn" key, then you may need to first press the "Fn" key and while holding it press the Command + F1. It all depends on how your Function keys are configured.

Otherwise you will need use Target Disk Mode as mentioned by @MrHoffman.

michellefromwellington wrote:

I am wanting to sell the machine as is but want to wipe the disks fully before doing this.

Wipe the internal storage using Target Disk Mode.

Transfer files between two Mac computers using target disk mode - Apple Support (ME)

Make absolutely certain you aim the erase operation at the correct disk.

Apple will recycle old hardware for free, as another option.

You’ll need either USB-A or Thunderbolt cables as listed in the article, or can use Apple to recycle it and trust in your passwords and any previously-configured disk encryption settings.

It’s quite possible the internal storage has failed too, which can prevent easy access to the remaining data.

michellefromwellington wrote:

This didn't work unfortunately.

It was a long shot. Even with Apple laptops it is not always easy or successful.