Any Ideas to RepaIr Loose Ceiling on NLcamper?

Thank you HMS Beagle. Your thoughts on removing that section means cutting the headliner fabric to remove the panel for access and gain a full spread of glue to both surfaces, is best. Esp. since bead board would not hold well with only spots of glue, would tend to break away versus fully spread glue.

I suppose one could apply a length of 2 inch wide hemmed matching headliner fabric to the cut seam. Sort of like trim hot glued to cover the seam of the headliner