External drives boot from the UEFI/BIOS one time boot menu, just like you boot live installer to do an install.
In UEFI/BIOS one time boot menu with newer UEFI systems you should have both a UEFI boot entry, if external drive configured for UEFI and/or a BIOS boot entry if MBR has boot code.
Some systems just have entries that say UEFI
xx or xxx where xxx is the BIOS boot. The xxx is name or label of external drive.
Others may have two menus, a UEFI section & a BIOS section.
Not familiar with your system.
Can you boot live installer in UEFI mode?