Let me just say, that as complex as vehicles get - I say vehicles, because all have changed, planes, trains, automobiles, trucks.
But as much as they have changed, they are
basically the same. i'll likely get flak for saying it, but most of what is cars today are add-ons. The engine block is for all intents and purposes the same, performs the same function as do the pistons, crankshaft and the flywheel.
One of the biggest impediments to automotive repair is to throw a $2.00 repair at a $0.25 problem. When a problem presents, it is best to start at the basic level to diagnose it and go from there. It is called Strategy-Based Diagnostics, really or some may call it process of elimination.
Now, the more highly trained a person is, one can also throw plausibility in there. When someone has a good knowledge of how a system works, they may be able to skip certain steps. In your case, if the headlamps are controlled by a fuse or fuses, that is a good place to start. Why worry about the switch or delay timer when the fuse is blown?
Why the fuse failed to open is secondary at this point. If the fuse is good it would have made sense to see if there was a voltage signal at the appropriate headlamp terminal. Why did I say signal? Voltage alone doesn't give enough information.
Let's say I am diagnosing this fault today. Checked the fuse - good, So I pull out a test light and I see I have a glowing filament. Well, everything must be good, right? Well, it is really sunny today so I may have not noticed that the filament was dim. I can get a test light to illuminate at some relatively low voltages. I put a DVOM in the circuit and I see I only have 5V; now, that is a problem - I have found a fault. Somewhere a wire is pinched or damaged and there is significant voltage drop. At this point, maybe I decide to take it to someone who knows more.
Perhaps you want to know why bulbs seem to fail too often. Perhaps when you connect the DVOM to the circuit with the engine off, the voltage is 12.6V. OK, so that is fine, but with the engine running the same circuit indicates 16.2 volts. That's a problem.
What I am saying is, all cars have high beam/low beam circuits consisting of at least two bulbs and up to four. In this case the high beam circuit indicates the switch is likely good, at least to a point. Now the weak point in an electrical circuit is always the mechanical portion, but for our purposes:
Follow the black arrows. All a schematic is - an electrical road map. Move the switch arrow to the left; you have Bat+ at the low beam socket terminal. You can diagnose other low beam faults from that point back. In that circuit, I'd be looking at the bulb(s) first, unless there were other clues.