Leaking coil = bad coil.

In your readings above, it appears the points were open since theres no voltage drop across the resistor nor coil.

To properly test your ign resistor, make sure theres no voltage to the ign circuit, disconnect both wires to the external resistor, change your VOM to read ohms in the lowest scale (like 0-10, 0-20 etc) then read across the resistor.
You want to see "some" resistance. Around 1.3 - 3 ohms is OK, over 3 ohms is bad and under 1 ohm is bad.

The coil should also read "some" resistance across the two low voltage terminals, the exact reading differs but in your case you need to replace it anyways since it's leaking.
The oil in a coil helps to cool it and once a coil heats up it's internal resistance will change which effects it's operation.

Good luck
Dave