Discovered today that water is leaking into the rear right passenger footwell. I think it's because the rubber gutter that runs along the top of the doors (on the car itself, not on the doors) is in bad melted shape. I searched, but can't find it online. Should i try to to apply silicone goop or butyl rubber or something? Anybody else have water leak in here during rain?
Water leaking here onto the carpet where this cotton rag is:

Expanded area view:

Closer view of slowly melting rubber gutter:

