Sudden 01 XJ electrical gremlin

My 01 XJ 4.0L AW4 132K mi while driving today with the AC on kept cutting out as the AC cycled. By cutting out I mean - the radio/ overhead console lights/sound turned off for a split second and the engine choked, but it never died. Never had an issue like this with any of my Jeeps, so I don't know where to start. Any ideas? Thanks

Battery voltage during the electrical surge? The headlights put a fair load on the battery, so try to recreate the problem and check if the headlights are dimming as well, or is it only when the A/C is on? I would suspect a bad alternator, or battery if headlights are dimming, as well.

Thanks. It's only when the AC is on. I've recreated the occurance several times. Doesn't happen when the AC is off. Don't know about battery gauge as it really is only a split second I loose power. And don't know re: headlights as I only drove during the day. Will test more tomorrow.

Use a voltmeter and measure voltage between the battery terminals when you cause the occurrence.

Try unplugging the a/c compressor and turning on the a/c switch while observing the voltage.

Try unplugging the blower motor and observe the voltage when you turn on the a/c switch.