I haven't had that particular piece come loose, but have fixed similar with 1/4" crown staples (short ones) and matching putty. There should be a strip of wood where that panel is bowed out. If your curious about wires, you can pull the recepticle on the other side of that and see a little in there, or use a bore scope to look in the wall. Lots of wires.
John and Rebecca Dickson
Emma-8 / Little John-5 / Iva-1+
2013 Ford F-350 Lariat FX4, CC LB PSD, DRW
2015 Jayco Jay Flight 28BHBE (#8)