You have the wrong solenoid. There are two types of 4 post solenoid. Large posts wire the same on both so the difference is in the small terminals.
1. S post (start) connects internally to activating coil and other end of activating coil is grounded internally to the case so when you apply start voltage the solenoid is activated. The wire from I (ignition) post going to the switch has resistance built in to reduce voltage on your 6 volt coil. When solenoid is activated the internal plunger applies full 12 volts to the I terminal increasing voltage to the coil for a hotter starting spark. You are wired correctly for this solenoid.
2. The activating coil is connected internally between S and I posts with no case grounding connection. One post is connected the voltage source, other post is connected to ground with start switch on one or other side.
Sounds like this is the solenoid you have.
On this one you should have continuity between S and I terminal, with both terminals open to ground.
On the correct solenoid you should have continuity between S terminal and case, no continuity between S and I terminal.
Get the correct solenoid and it should work.