Todd,
RV putty tape, or butyl tape will work to seal the screw holes.
I wouldn't trust just a rubber strip to seal the screw holes.
The rubber strip is used to keep water from coming in around the center of the hinge, as it is not designed to be waterproof, like a hurricane style hinge.
I'm not familiar with what your trailers manufacturer used originally, but most in that era used a strip of the most waterproof canvas available, and wrapped the hinge, sealing the canvas at the top.
Most also used a strip of rubber, or other material to separate the two types of metal; steel hinge/aluminum skin, which may be what you're seeing?
If the rubber under yours went all the way and the hinge was installed flat, then that may be a good option to replicate.
These pictures may help to explain the canvas wrap.
Rob


Waiting for "someday" will leave you on your deathbed wondering why you didn't just rearrange your priorities and enjoy the time you had, instead of waiting for a "better" time to come along...