Plotting current against voltage for the amber truck side marker lights produces the expected straight-ish line:
The slope suggests a 330 Ω resistor, but the internal PCB sports a pair of 150 Ω SMD resistors.
I don’t believe the X-axis intercept for a moment, but 1.5 V seems about right for an amber LED.
Oh, and the DMM fuse doesn’t have a ceramic body. You’re seeing the vaporized remains of a 315 mA fuse neatly deposited over the inside of the glass tube after being shorted across a 3 A bench supply.
I hate it when that happens. Replacing it emptied the little bag of those meter fuses; next time it’ll get a half amp fuse.
The Smell of Molten Projects in the Morning 
I got a chuckle out of this picturing you shotgunning fuses. I remember a picture from a college text book showing a tech at a bench with a pile of parts on the ground indicating they were “all” bad.
Flashbulbs and fuses: they’re so hard to test!
The way I see it, meter fuses never get overloaded by a few percent: the current is either just fine during a measurement or oops too high with the leads crossed. A 10 A fuse wouldn’t be appropriate, but a factor of two doesn’t matter.