The ignition switch rotary assembly, the ignition switch consists of the key barrel and behind it is a rotary switch.
The switch is what connects the circuits based on key position.
In worn condition they tend to not make (proper) contact.
Get yourself a wiring diagram of your application and a multimeter.
Set the multimeter up to measure voltage on the IGN wire on the starter relay, when you throw the key to crank the engine you should see a 12volt supply coming on that wire.
If there is no juice it means the ignition switch is not passing the 12volt signal to the relay.
If you do get 12volt on the relay you can exclude the ignition switch and start sourcing your issue in the starter relay. (find a replacement)
From what i know is that it's more likely the ignition switch that is faulty if it is a random start/no start, if the start relay is bad it mostly will not work at all.