Since your Truck Camper is going to be plugged into electricity you should have no problem running the refrigerator on electric 24/7. You could also run the refrigerator on propane, but you would have to keep an eye on the propane level.
Unlike the refrigerator in your house the refrigerator in your camper is an absorption refrigerator and has no moving parts like a compressor so it uses a lot less electricity than the fridge in your house. That's the good news the bad news is that absorption fridges take a lot longer to cool down when first turned on than a home refrigerator. Take a look at the video below so you can get an idea of how absorption fridges actually work.
Also unlike the refrigerator in your house the fridge in your Camper requires a little more maintenance. Take a look at the video below to find out what you need to do to keep your RV's fridge in tip-top shape.
Lastly, since I do not know the make, model or year of your camper's fridge I need to make you aware that there have been several recalls for RV refrigerators due to possible fire hazards. Before you actually leave your refrigerator on 24/7 you should check the links below to see if your fridge is subject to any of these recalls.
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