As Daniel says, the band was originally strictly decorative (and was a more economical way to deal with the seam at the factory). I say "was originally" because as they age, they often become a liability (as outlined in previous threads).
Since we're going into it here, I'll quickly summarize how the trailer was built. I think that once you understand the belly-band set-up, you'll be better able to judge the various options and choose the one that suits you.
So, the trailer has upper and lower molded halves, as if you sliced a hollow ball in half around the "equator." At the factory, they bond these halves together on the inside with fiberglass cloth and resin. As such, it's essentially permanent and waterproof, and you now have a "whole" ball.
But then.... they have a cosmetic seam on the outside, like a crack, running around the equator. It's completely possible to 'glass and fair this so that it disappears, but that is time consuming and requires a certain degree of skill and artistry. Our eggs were built to be economical. So what to do?
In comes the belly band. The belly band will look good, and can run around the equator and cover the "crack" on the outside of the trailer. It can also be installed quickly and by your basic worker with a rivet gun.
Now we have to back track in our theoretical Trillium building because we need a way to anchor the rivets that hold the belly band trim on. Holes going all the way through into the trailer would not be a good thing. So what they did was the following (I may have slight variances in the order of things since I was not at the plant, obviously, but I believe my overall concept to be correct):
1) They put the shell halves together, and then probably put on one layer of the fiberglass "tape" on the inside of the trailer. A first layer of bonding. Probably while the resin was still wet, they stuck mild steel plates, of about 1" square at equal distances around the trailer on the inside of the seam.
2) Now they went to the outside, and riveted the belly band trim on. The rivets (at this point) went all the way through into the inside of the trailer, catching on the mild steel plates.
3) Now back to the inside, where they laid on another layer (or a few layers) of resin soaked fiberglass cloth onto the seam, thus encapsulating the belly-band-rivet-backing-plates of mild steel.
So, although no water can leak into the trailer, over the years water could seep into the rivet holes of the belly band and get to those mild steel plates (if only they had not put those in...). The plates then rust, expand, and NOW you can have leaks
if the expansion cracked some of the fiberglass tabbing (the "tape"). Or, if a rivet broke and someone re-riveted a section, well, they might have riveted all the way through into the interior (ask Barry about that....
So now you see how the trailer was built, and how the belly band was installed. I'm thinking this should assist you in deciding what measures to take, and which will be useful.
If you want to reproduce the original belly band set up, and assuming there is some deterioration of your plates, I would think you would have to (or would want to) go from inside and "do it right." I would imagine something like the following:
1) Peel back ensolite and tape it out of harm's way.
2) Drill out rivets from outside and remove belly band.
3) Clean up outside seam, removing all caulking and contamination (including mold release wax, with something like Interlux 202).
4) Dig out probably-rusting rivet backing plates from inside. Decide after seeing condition of things whether to just put in new plates (non-corroding!) or whether you need to do any repair work first.
5) Re-attach belly band with new rivets.
6) Smooth over any protruding rivet ends on inside and prep
7) Put a few layers of fiberglass tape/epoxy resin on inside of trailer and wait for it to cure
8) Wash off amine blush and dry, then re-adhere ensolite.
9) Whether to caulk outside of belly band? Your call, knowing where the water can go or not go.
That said, it's not how I would choose to go about the repair, although I understand the urge to be original, and how one might choose that.
I guess for me, knowing that "original" was partly chosen to be cost-effective, well, that makes it easier for me to go in with an improved set-up. But original is cool too