On judging the electron emission of an electron tube by simple means

At your risk.
Take all safety precautions.
Always use a suitable fuse in series with a battery for injury or fire hazard protection.


The simple idea is feeding the heater with heater voltage through a suitable fuse.


Then measuring with a high input impedance voltmeter the potential between reference cathode and grid which would be negative if cathode emits electrons. And the more electrons are emmited the more positive would the cathode be or less negative would the grid be.


Further reading:


Operating features of the Audion - E. H. Armstrong - 1914