So, I've made a bunch of progress, and she's coming along nicely. However, she's manifested a new issue: the left low beam either comes on, flickers, and goes out, or doesn't come on at all.

We checked for the lead wires fusing together issue, they look fine. Replaced the bulb, didn't help. Checked power at the bulb, no power is getting there.

Is there a fuse specific to the driver side low beam? Or am I missing something else? I read through a bunch of threads and didn't hear anything specific to what I'm describing.

Relevant: It's the HID headlights.

It could be that the ballast for the left hand light is breaking down, I'm not sure how easy it would be to swap the ballasts from one side to the other and see if the fault moves as well.

It is easy if like me you have aftermarket hids fitted.

On the subject of checking for power at the bulb I would be very wary of doing that with an hid set up because of the high voltages involved.

Are you sure they are HID ?..I don't recall 2002 ever having them unless they are aftermarket.

in either case:

You probably have a bad ground connection to the car's body..check the bolt nearest the lamp assembly that is screwed into the fender wall it will have a black wire(s) attached to it...Loosen it and screw it back in tight...With your salty environment this is a common issue.

I have a 2002 x-type with the HID OEM variant. First check the igniter by swapping with the other light that is working. If that doesn't resolve it check behind the light and make sure the 3 wires connected to a screw on the metal body are tight and clean.
If you have a good ground and the igniter doesn't resolve it then it is probably the ballast. Bad news is the ballast is mounted on the underside of the light assembly and can only be removed by removeing the light assembly. Removing the light assembly requires removal of the front bumper assembly. The light is bolted on and only accessible with the bumper cover off.
The fuses are 16 and 17 in the engine compartment fuse box

I forgot earlier to attach the parts blow up for the HID headlight.
You need to take the working bulb and igniter and install in the non working light to know for sure it is the ballast.
If it is let me know and i can give you a good vendor for replacement.