max_5gen wrote:Check you battery voltage I bet it's too high. One of the maxima owners had the same problem on his 2k2 Max and it turned to be bad contact of the alternator connector. Check it and clean and then see what happens.
Too high? Never heard of that before. Flickering or intermittent battery and brake lights together are usually a sign of LOW voltage. Often it's a sign of alternator failure, especially when the vary with RPM the OP describes.
Use a multimeter to test voltage at the battery terminals. With the engine running, you should read ~13.5-14 volts. Anything less is likely a sign of a bad alternator. Make sure when you test that all doors are closed and lights are off. You can also try testing with the car running and headlights on. The reading SHOULD be the same as above, but may read less, which would be another sign of failure.
If you decide to take the car to an auto parts store or similar to have the alternator and/or battery load tested, keep in mind that alternator issues can be intermittent and VERY hard to track down. Alternators will often test good even when definitely bad. You sometimes just have to get lucky with the load tests to "catch" the problem in the act.
If you do have a bad alternator, the battery won't be charging correctly so the car will likely eventually fail to start. You might want to make sure you have a set of jumper cables (or, better, a portable jump-start power supply if you have one) in the trunk in case that does happen.