You can't use an ohmmeter on an energized circuit and expect to get meaningful readings. The meter supplies (injects) it's own power and external power will alter its measurement capability.
In-circuit ohms measurement, requires the tester to control all paths of current flow.
The coils are conductive and have a common attachment to each other. They also attach to the points.
In other words, both point contacts have a path to the other point contact. If you are measuring contact resistance you must account for, or eliminate alternate paths of measurement flow.
Cheers,