Basically you'll be looking for an electrical problem following a path/pattern; from the bulb to the points in the wiring harness that divert power from the battery and the alternator. These instructions isolate the cluster panel board. If you have trouble making sense of this, please reply with questions. Other members, please pipe-in and correct me when I'm wrong. No matter how much I know, it seems I can always learn more. You may need to re-read this:
1. Check your fuses (if you haven't yet). It could be a 40A, 50A, or 15A fuse that leads to the lighting. There is one in the underhood box. I'm not sure if there is one or more under the dash, so check those too.
2. If those are good, then we need to see if the bulb is getting power from the wires that lead to it. With the aforementioned instrument cluster out, remove the bulb.
3. Put your keys in the ignition and turn the key to the accesorry position. Your engine doesn't need to be running (unless you got a bad battery).
4. Pull back on the dimmer switch.
5. Confirm your high beams are on.
6. Use a multimeter to test the leads going to (not from) the cluster panel. You should get 12 volts or less (if you know the actual number, please reply with it!). If the readout is negative, you have your test leads backwards. If you get no volt reading, no matter if the test leads are backwards or right, then you certainly know there's something wrong. Take note of which wire is hot/positive. The hard part comes in trying to find where the problem lies; that's why I like following a pattern. Theoretically, a problem could be between the lightbulb socket and where the alternator &/or battery sends power to the cluster. It could be something wrong with the cluster board or in the wiring (or worse, both). Make sure there's no corrosion on the leads where the lightbulb fits. I'll get to isolating the cluster board later. There could be a grounding problem.
7. If you're not getting any voltage reading whatsoever then you need to check for resistance (congruency) in the same leads you just tested.
8. Switch your multimeter to Ohms and check the resistance of the multimeter itself & note that number.
9. The same way you tested the leads to cluster panel the bulb for voltage, test for an Ohm reading. It should not be infitity and it should be higher than the number you just noted.
10. If you get a voltage reading from the pig tail/connection going to the instrument cluster pig tail, that's a bit of good news. That's what I would expect. So now we have to test the instrument cluster.
11. Plug in the instrument cluster back in and repeat the tests with the leads to the lightbulb. I'm sorry, before you do that, leave it out and check the cluster board for congruency (done by Ohm reading). That maybe not feasible if it has more than one pair of wires going into it to power the cluster board. If there is just one pigtail that connects to power, one hot lead will be in the pigtail (attached to the cluster panel that you disconnected). Hopefully you know which one from noting the hotwire from the aforementioned step six. Attach the red lead from the multimeter to the wire that gets power. Attach the other, black, lead of the multimeter to the + side of the lightbulb socket. If you're not getting congrency, that's a sign it's a bad cluster board. If it's a bad board, you can replace it or have automotive electrician see if he/she can fix it. Fixing boards isn't typically done at a person's residence. Unless you are an electrical engineer, an automotive electrician, or you fix boards to earn money. A good tuner who works on ECU's maybe able to fix a instrument cluster board.
If you're not getting volts to the cluster, but you have congreuncy in the cluster board, that doesn't mean your cluster board is bad. However, If the cluster board is getting power (volt reading from the connections coming from the connection from the wiring harness) and it doesn't have congrency then it is bad. Reconfirm this buy plugging back into the wiring harness and test the leads of the lightbulb socket for volts and ohms.
Oh yeah, checking the ground wires for congrency is how to test for grounding. The way to test for grounding on the board is to attach the red test lead to the negative lightbulb socket and attach the negative test lead on the end of the negative lead in the pigtail (the lead that's not hot). You want a higher Ohm reading than the Ohm reading than the Ohm reading you get from touching the multimeter leads together and you don't want infinity or zero.
If the instrument cluster board is fine, then you're gonna have to go deeper down the "path". In the meantime, I'll look for a *good* wiring diagram to reply to this.