What would be useful is some sort of indication on the desktop that system is running in live mode vs persistent mode.

This is to inform the user about the mode and not having confused the wrong startup option and believing to have booted another boot option. Would be bad if someone thought it is persistent, but accidentally chosen live and then loosing data. Or chosen persistent but wanting to choose live and then persisting data not wanting to persist.

What about a persistent checker systray...?

Colors:

• green persistent indicator systray for persistent mode
• red persistence indicator systray for live mode

Autostart:

• persistent: no, don't autostart persistence indicator systray
• non-persistent: yes, autostart persistence indicator systray

Reference:
https://www.whonix.org/wiki/Whonix_Live

For now, this is Non-Qubes-Whonix only as per:
https://www.whonix.org/wiki/Whonix_Live#Live-mode_on_Qubes