Puzzler for you electrical gurus....

OK... not a guru, but still feeding back to you based on your observations:

You state: "I unplugged the camper from shore power and now the light strip works! When I plugged it back in the light strip went out. Now, why would that be?"

Check the leads with the camper on shore power and use the voltmeter on the 120V AC setting to verify if it is 120A and not 12D being supplied. Perhaps there is some weird "auto switch-over" to 120 when plugged in that is not there when disconnected. Perhaps it reverts to 12DC when unplugged on that circuit.

ON EDIT-
I reread where you also state: "Voltage is the same at the leads whether or not the camper is plugged in!"
upon reading that I am stumped too!

Could there be some sort of current sensor on the LED's? That is, there perhaps is higher current available at 12V when plugged in that is not available on the house batteries??? I do not know what else could be causing an on/off switching condition between shore and 12V power inputs.

This is a good one!

Figured it out - but still stumped!

Per the above suggestions, I went out with my multimeter and checked the wiring. As HMS Beagle said, on my Bigfoot the black is hot and the white is ground. Voltage is running 12.9 - 13.1. Just as a check, I reversed the leads (in case the light strip got wired wrong) but nothing.

Then on a hunch, I unplugged the camper from shore power and now the light strip works! When I plugged it back in the light strip went out. Now, why would that be?? Voltage is the same at the leads whether or not the camper is plugged in! And the original light fixture (has an LED bulb in it, by the way) works whether the camper is on shore power or on battery power.

White wire as ground is fairly standard in an RV, a hang over from houses where white is neutral and black is PH1? Sometimes you run into black and red which would be - and + on a car or boat. It never hurts to test it.

Yep, had the same problem when I was putting LEDs in.

Don't use a test light to check the connections. A lot of RVs don't follow the standard electrical code.

On mine, + was black, and negative was white (crazy stuff).

On a standard voltmeter, the red lead is the positive, and the black lead is the negative, when plugged into the correct red and black terminals on the voltmeter (check that too !).

The red wire when connected to the positive, and the black wire when connected to the negative should give you a positive 12ish volts (depending on the battery charge).

If it is negative voltage (little - minus sign is displayed) , then you have the red wire connected to the negative, and the black wire connected to the positive. That's how you know on a voltmeter. Test lights don't tell you that.

Hope this helps !

I suspect the 12V wires are reversed at the old fixture. Just reverse your connections and see if it works.

Rather than use a test light at the source, use a volt meter (digital if you have one) and take an actual reading. If the source is less than 12 volts then perhaps it is enough to power the test light but maybe not enough to run the LED??? I dunno if this makes sense, but I am trying to ascertain a possible answer from the facts you provide.

Try reversing your connections. Standard RV / automotive bulbs don't care which way the electrical current flows into them. LEDs have to + to + and - to - for them to work.

Bill