I had the same thing happen to me on a mitsubishi colt years ago,I spent ages trying to figure it out.
My mate came over and knew what it was in about 30 seconds.
Exact same thing, little white resistor thing on the firewall.

public transport- thats why i ride a bike- hate paying to ride in a cattle cart to work not on time

I jumped in the 120Y this morning to head off to work, when it won't start. At first I thought I'd just flooded it or used too much choke, but after a few minutes wait it still wouldn't fire. I noticed that the engine was starting but stopping as soon as the key went to 'ON". I came to the cocclusion that the ignition switch must have failed overnight. So I grabbed another one out of a Sunny rolling shell I've got, still the same, will start in the 'Start' position, but not when it goes back to 'ON'. At this time it wass getting late, & if you don't work Friday you don't get any Saturday overtime, so I got a lift to work with my Father. On the way, I was thinking about the problem, & realised the problem was the car wan't getting any power through the resistor, when it went to the 'ON' circuit. When I got home this afternoon, after a short recovery period I needed after 'Public Transport'ing it home, I removed the resistor & there it was. The wire coil inside the resistor had broken. So I found an old resister, fitted it in place & we're back in business. So, if the same happens to anybody else, check the resistor first, before you got tracing wires. The clue is if you can get the engine to run by holding the key half way between the 'ON' & the 'Start' positions, it's not getting any power through the circuit that goes through the resistor.