Performed some experiments tonight with unexpected results.
My friend sent me the two 8971s in question. One is a fine grid, one is a coarse grid tube. Both reportedly exhibit the same "partial illumination" problem when running in the black emerald clock. So I began by cleaning and labeling the two tubes. I then took my black emerald, removed one of my good 8971s and installed a faulty tube in the rightmost "seconds" position. Sure enough, partial glow as expected. No matter how long the tube ran, it was always partially illuminated.
My first plan of attack was to use the source measure unit (SMU) to apply repetitive high current pulses to all the cathodes. The 8971 datasheet describes the maximum current of all cathodes simultaneously to be limited to 14ma. I set the SMU to operate in pulsed mode and zapped the cathodes in pairs of two (anode connected to positive, two cathodes connected to negative). The pulse per set of two cathodes was delivered as follows:
75 milliseconds period (between pulses)
50 millisecond duration (per pulse)
200 pulses total
0-200 volts peak to peak
current compliance: 14ma
After making sure each cathode pair (randomly chosen) got a cycle of 200 pulses, I reinstalled the tube into the black emerald. During the first 30 seconds, the segments began to come back to life. After a minute, the questionable tube was illuminating normally. I could not believe it. Did the cathodes need to be "revived" somehow after a prolonged (30+ years) period of inactivity?
I set the experimental tubes aside again for an hour, to let them "cool" off, and make sure the effect was not temporary after having warmed them up with the high current pulsing. Sure enough, I inserted them into the black emerald and they resumed functioning as normal. No more fizzling out.
As exciting as this is, the results are still very preliminary. I will provide further updates once they have been mailed back to the original owner and he has a change to try them out. Then time will tell if they are truly resuscitated!