Home Improvement

Without seeing it, the best solution I can think of is to try cleaning it up real good with something like Simple Green(works amazing on rubber). After it's nice and dry, use some Eternabond RoofSeal tape making sure to have at least two inches overlap. That stuff will stick well to clean rubber and hold good for a few more years. Nothing will ever be a permanent solution until you can replace the whole piece of rubber roofing unfortunately .

For near-vertical mansard roof shingles, I think they use a combination of lots of nails and plastic cement.

This is a use case for a step flashing or pan. Use sheet metal cut to shape and bent at a right ( or other angle) to give you a nailing surface. You nail it to the roof deck and it stands up.