Duette;

This is a highly unusual fault condition, as when the engine is running, there are two power sources in the vehicle...the charging system, and the battery...and for both of them to fail at the same time, and then return to normal is damned near impossible! Its more likely that a common failure such as an intermittent connection is taking them both offline, but I have trouble imagining just what this might be *...so I will make some general recommendations:

1. As a preventitive, after disconnecting battery, disconnect, clean, prepare with anti-corrosive zinc compound, and reconnect all the usual suspects like battery, fat starter stud, chassis/engine strap, generator/regulator, ignition switch, fuseblock...

2. If symptoms persist, temporarilly mount a voltmeter, and connect across the battery (RIGHT TO THE POSTS **) such that you can glance at the meter to see what the actual battery voltage is...I expect it should show 12V...try the lights again...if they don't work, this suggest a disconnect and helps narrow the failure considerably. Report back with symptoms and what you find. ** disconnect vmeter when parked to prevent discharging bat.

* I did have a similar problem years ago when the contact block in the solenoid failed (apparently became disconnected from its mechanism), fell between the battery connection and the housing...this brought down the whole electrical system with its tremendous load (not by disconnection)...so much current flowed that the battery cable got hot, and even oily grung on the chassis to engine ground strap started burning up, the temp needle took of because the metal capillary tube even flowed its share of current...but a quick "Chinese Fire Drill" to disconnect the battery saved the Sow Weasel from burning up... Exciting!...

Good Hunting
I'm Ron Kwas, and I hope John Mc. approves of this message too...I sure as hell stand behind it!!