You indicated that the previous owner indicated that there is no battery and that you cannot find the battery so perhaps it/they were removed and not replaced. Find the battery charger and note the size and color of the wires, usually red for positive and black for negative; than look where the battery is supposed to be and see if you can find the wires. If you find the wires and they are not attached to anything you have found the problem, no battery. Since the lights work on shore power you know that the converter (120Vac to 12Vdc) is working correctly. So, the problem is probably no battery which is also needed when the engine is running to power the 12Vdc system. Also, if you go on the Keystone/Dutchmen website or do a google search for the wiring guide used by Keystone/Dutchmen it will provide the color coding scheme that identifies which wire does what. Here's the website: https://www.keystonerv.com/innovatio...r-coded-wiring
For a basic understanding of the electrical system in your RV watch the Keystone video at:
Hope this helps you solve your problem. Have a great time on the road.