In my humble opinion, nails have little purpose in construction of a deck. There are at least five different types of screws made specifically for this application. They have torx heads and are very solid. Only specific instructions I would otherwise have is that if you really want to press the old and the new sisters together, drill a pilot hole in the side ...
Adding a sealer to the surface does not sound like a permanent repair - may last a few seasons...
Covering the whole roof again does not sound like a reliable solution. Will this treatment do the 70years the original surface did?
I would look at opening that joint by removing the rivets / screws whatever the fixing is, then re-doing that seal and refixing ...
It’s part of the weather-tight system.
It’s not designed to STOP moisture, but rather CHANNEL moisture that may enter during a sever storm. Rather than have beads of water laying along the edge, the plastic cover will channel the moisture to a drip edge on the skylight.
I agree with @J. Raefield, glue it back in place and make sure the edges are sealed.
Nothing on the inside like that would have any purpose related to water entry; if the water got that far in, there would already be damage. That is, at best, just draft and heat loss, but most likely it's just cosmetic. I would just glue it back in place.
I'll tell you what I did with my deck and it worked great... The product name is Copper Green-Brown
Copper-Green 1 gal. Wood Preservative
I just retreat it every 3 years ( no stripping needed ) and it looks fantastic. Very simple solution 👌👍