[n240sx]

I went through something very similar earlier this week. The starter only clicked when attempting to start the car, however the starter would engage every time 12v was applied directly from the battery. It turned out to be the blue relay in the engine bay even though the relay clicked when bench tested and read electrically continuous with multimeter. Before replacing the relay, I tried replacing the ignition switch and bypassing my alarm with no luck. As a last effort, I removed the relay and jumped the larger relay connector terminals and the car started with the ignition switch. In hindsight, I should have tried this first because it is a very simple test, but I did not expect my relay bench testing results to be misleading. Replaced the relay and now the starter engages every time I turn the key. It seems the relay was incapable of sending enough current to the starter possibly due to corrosion on the internal contacts. Hope this info helps.