Gm is short for mutual conductance (1/R), or if the grid volts changes by 1V how many mA the anode current changes by. With push pull output stages, while the anode currents could be equal between the valves, they could change by a different amount for the same voltage changes on their grids. Because of the equalising effect of the output transformer, the added distortion is very low (>.1%?). The standard British valve tester was made by Avo. it had a test buton which tested the gM. The only way to test the "life" of a valve is to see how much residual life there is left in the cathode, to do this you have to reduce the filament voltage by a relatively small amount, say .1V. if the filament is capable of oversupplying electrons at 6.3V, reducing the fils to 6.2, should still supply enough electrons for the normal operation of the valve. A test button would work but it must be held in for say, 30 seconds to allow the filaments to cool to their new operating temperature, so the emission of the cathode also falls to its new level.
Frank