You are correct that the negative side of the coil shouldn't 'light up' when the points are closed.
Leave the key on and points closed.
Pull the distributor cap and touch movable arm of the points. If no light, the wire from coil - to the movable arm is bad. If light touch the light to the fixed part of the points.
If still light, the points are not grounded. If no light the points are bad.
'57 GMC 102, Original 347 V8, HydraMatic, 3.08 rear gear, added A/C, disk front brakes, HEI, AFB carb, '98 Honda Black Currant paint. T-boned and totaled 10/12
'52 GMC 152 Stake Bed, Original 228, SM420, added A/C, HEI, disk front brakes, '67 Chev 3.55 rear gear. Gets used as a real truck.
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