Here's just a quick thought. If you do have a high drain on your electrical system, and your stock alternator is in less than perfect shape, those lights could have been pulling your voltage down to about the cutoff voltage for the headlamp relay. This sounds dumb but just hear me out for a sec...
The headlamp relay (or any other relay for that matter) is an electro-mechanical device, meaning it is a mechanical switch that is controlled electronically. When power is applied, the switch is "closed"; when it is removed, the switch is "opened" again by a spring that is weaker than the coil that "closes" the relay.
Now, all relays have a specific "cutoff" voltage. The cutoff voltage is the MINIUM voltage that the relay will reliably hold a "closed" state or position. Any less, and the relay's coil will not make enough magnetism to hold the contacts closed against the pull of the return spring, and the relay will not stay "closed".
This is usually an undesired condition caused by draining the source battery below the cutoff voltage, or by simply drawing too much power from the source at one time. In your case, if you’re bulbs (in conjunction with your other electric loads) were actually pulling the jeeps charging system voltage down to the headlamp relays "cutoff" voltage, you would actually hear the headlamp relay make a squeal noise as long as the voltage remains at this low level. Once the electrical system is taxed less (turning some crap off) the squeal will get lower pitched/quieter/ or disappear all together.
To explain why the relay squeals when it's operating at or just slightly above it's cutoff voltage, think of how the system works for a sec.
The headlamp relay is controlled by your headlamp switch on the dash. The headlamp relay allows a small amperage switch to control a high-drain load, like your headlamps. The relay itself pulls it's coil voltage from the same source as the headlamps do. If the big, high drain headlamps lower the charging system's voltage to about the coil's cutoff voltage, the relay will not be able to hold the contacts closed. The headlamps will loose power and the voltage will begin to rise again. If you don't turn the switch off, the voltage will eventually raise to the point that the relay will then fire again. This causes the headlamps to draw full current once again, and thus, causes the voltage to drop again to the relays cutoff.
Now, you might be saying "yea, but I don't see my headlights blinking on and off..." no, you won't see them blinking on and off. Do you see the lights in your house blinking on and off? No. But the voltage going to your house lamp actually drops to zero and then reverses it's polarity. You don't see it because it happens 60 times per second. The bulb never gets a chance to cool and stop producing light. What you see is the average of the bulbs "brightness" over a wide range of voltage. In your jeep, if you are actually hearing the relay squeal, then the relay is letting go and closing again (or thrashing) many times a second. The headlamps will not blink on and off, they will stay steady, though a touch dimmer than usual. Also, since the average of the voltage you're feeding them is lower than it should be, and since you are feeding them a rippled DC current, the filament will receive much more exercise then normal... this will DRASTICALLY shorten it's life.
Your relay's coil could just be week too. That would cause the same problem if your charging system ended up testing good and not being the problem. If that's the case you'll have to get one from the bone yard (or a new one if you prefer).
The ground connection to the headlamp relay's coil could be bad too. This would cause low/unreliable voltage at the coil which could cause the relay to thrash as well.
Of course, there is always the possibility that any one of the connections on the control side of the relay could be bad/intermittent. The relay coil ground wire is usually the culprit though.
If the relay overheats and/or the wiring to the headlamps themselves is hot while this is happening, the ground's for the headlamps could have high resistance causing the headlamp circuit to drop more voltage than it should. This could theoretically cause the voltage drop and cause the relay to thrash too, but usually if I see something like this happen, it just welds the contacts of the dang relay together and the headlamps won't shut off... same with cooling fan relays...
Man, sorry I wrote such a long post. I hope I explained my point so it actually makes sense to normal people.
