The behavior of starting at a specific resistance and climbing is characteristic
of capacitors - the initial resistance is the leakage and as the capacitor
is charged by the meter's sensing current the apparent resistance goes up
until it matches the voltage with which it is being charged.

Since the starter solenoid is hooked directly to the battery cable, if you
have a separate starter switch hooked only to the starter it is not surprising
that you can engage the starter with the key off. But unless the ignition
and FI are powered, it won't start.

I didn't see what kind of ignition switch you are using but if it is an old OEM
switch, all kinds of funny things can happen inside as they get old, including
internal shorts, resistance contacts, no contact, and even burning lubricant.
(this list is based on my experience with old ignition switches.)
That's why the later models have replaceable switches. I replaced one on my
164 that had a hole arced in the metal can, for example.

The best way to find out what the wires are is to disconnect them and check
them one at a time against ground. You can even do it with a light bulb.
At least that will show which ones are powered. With them hooked up you are
confused by whatever they are hooked to.
--
George Downs Bartlesville, Heart of the USA!