If the points are closed the voltage should drop. If they are open it should stay the same.
There may be a chance the wire from the coil to the distributor is grounded where it passes through the distributor.
hard to tell from the picture of the distributor, but looks like inside the housing where the points attach to the bolt that goes through the housing, it may be grounded to the housing. It should be insulated from the housing.
Take the wire from the negative side of the coil off the bolt at the distributor housing. Turn the switch on and see if you have battery voltage or close to it), at the end of the wire while it is loose from the distributor. Then touch the wire to the bolt that sticks through the housing and see if the voltage drops while the points are open. If the voltage drops while the points are open, then the points or the bolt where it passes through the housing is grounded. The bolt that passes through the housing must be insulated from the housing. The spring from the points connects to this bolt.
The only time the points should be grounded is when they are closed.
