Car won't start - bad ignition switch?
The yellow wire at the start relay should get 12 volts evey time the ign' switch goes to the start position. If it does the switch is good. If the relay doesn't click and engage the starter every time. the relay or the neutral safety switch is the problem. Next test is short the relay terminal the brown wire is on to ground. If the relay now clicks every time the switch goes to start without fail the neutral safety switch in the problem.
If the relay doesn't click the relay is the problem.
If you don't mind throwing a few dollars at it, forget diagnosing and replace the relay.