The grid in a 3-500Z is a cylindrical cage with vertical wires joined by a 'belly band' wire at the top, middle and bottom. If the grid runs too hot, the weld holding the end of a grid wire will break. The free end of that wire will curl enough to touch either the cathode or if you're luck is REALLY bad, it will touch the anode.
A continuity test that has a beep feature can reveal this short if you clip the meter probes to a grid pin and one filament pin. Hold the tube sideways and slap the tube on the side as you turn it 360 on its lengthwise axis. This will evoke a brief beep from the meter if a loose grid wire touches the cathode long enough.
There are other, more-sinister and more-expensive faults that can peg the grid meter. Just don't select "grid" on the meter knob any more until the problem is fixed. Heathkit included no protection whatever for the grid meter. A tube fault can blow out the meter's coil. Bad day when that happens.
A tube with a loose grid wire is the most-likely cause, but not the only one.
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