What year Scamp
and do you actually have "Rat Fur"?
I have seen some people ask about it and they think they have it but they have vinyl or something and are calling it Rat Fur?
If it is Rat Fur and is Hairy and soft????I would try to use a Drapery Hook that you slide into the furs backing and fasten to that with something very light weight
Luckily you can get very light weight
LED fixtures and you could Wire Tie them to a Drape Hook if needed.
I too a different approach in my Casita
and wrapped the perimeter at ceiling height with LED Rope Light.
It provides a nice light throughout the trailer.