1998 Legacy Outback Dashboard Illumination

Been having a problem for a while now, but until recently, it was so
infrequent that I wasn't entirely sure I wasn't imagining it.

While driving at night, my dashboard lights have been going out. It
happens at an irregular interval, and they won't come back on by
themselves, but toggling the headlights on and off always resets it. I
think it only happens while the car is moving, but I'm not sure, since
I don't always notice right away (Have to keep most of my attention on
the road, obviously). The headlights stay it, and the indicators
(speed, tach, heat, turn signals etc) all still work. Most
surprisingly, the radio also stays lit (I've got an aftermarket radio
that goes completely dark when the headlights are off). The only
lights that I know are going out are the illumination for the
instrument panel and the lighting on the automatic transmission
shifter (the little lights that tell you what gear you're in. I can't
be entirely sure if any other lights are affected, because a lot of
the console lights have burned out over the years. I am pretty sure
the cruise control switch stays lit.

It's gotten markedly worse this week, though I don't know if there is
anything to that. It's been colder this week, and on Saturday, I hosed
down the engine, if that could be responsible.

Based on the wiring diagrams I've looked at, it looks like the wire
coming from the illumination fuse splits into a yellow/white wire and
a (I think) green wire, and the fault is somewhere on that white/
yellow wire.

What I want to know is where should I be looking for something to be
wrong, and what sort of wrong is it liable to be? I know in principle
where this wire goes, but I don't actually know physically the route
it takes to get to the various parts of the car. I'm also really
perplexed by the fact that when the lights go out, the *only way* to
make them come back on is to cycle the headlights on and off. What
should I be looking for, and how much disassembly of my car am I going
to have to do? I'm reasonably handy at this sort of thing, but I have
a lot of time commitments and will have to find a mechanic to do the
repairs if it takes more than a couple of hours -- and this looks like
it might be a painful sort of hunt-around-for-a-bad-wire type problem.

Anyone have any experience with this problem and know about some kind
of trick to make the fix easy?

Or heck, if there's some alternative to actually fixing it properly,
like maybe and easy place where I can hook the dashboard lights
directly into the cigarette lighter or something

Thanks as always.