It would be a lot more intuitive. Even knowing exactly what was being described and how - It still is difficult for me to understand a graph in which Time is on the Y-axis. I considered for a few moment that I was actually being trolled with that graph.

Definitely. Also choose colours that aren't almost identical.

The blue and black don't look very close to me, and they're pretty color-blind safe. Odd.

Don't underestimate the damage of bad screens, bad screen settings and people blaming the source rather than their setup.

It's all right to blame the source. Imagine half a population having grayscale screens. Would you pick colors that map to the same shade of gray? I guess not, so why would you pick colors and thickness that can be mistaken on so many setups?

In this case it doesn't matter, as it's obvious which line is which.

Even just laptop screen brightness or glare can play a huge role here. I know it's offtopic, but if anyone is aware of a guide or methodology for picking colors that will be less susceptible to this problem, I would love to see it.

'Cheat' and use something else to differentiatie between the two, in addition to color (line thickness, line dash, markers)

You probably should always do that, as you won't know where your chart will be used (printed in black and white, very lossily converted to JPEG, whatever)

Convert to grayscale.

colorbrewer

I cannot tell them apart, other than length.

Be nice to have one solid, the other dashed or dotted.