The guy I bought my San Jose build 65 GT Fastback from pressure washed the engine compartment prior to my buying the car. He didn't do that good a job. I remember that there was a small piece of what looked like masking tape attached to the bottom left of the blower that I knocked off when I replaced the heater core. That was 19 years ago. I have a "Dec 2 1965" dated motor sitting on my desk as I type. You can see the remnants of something in one spot about three inches long. It is 15/16inch wide. I just removed a painted over 1/4 inch chunk. Whatever material it is, the color against the motor housing is light brown (almost rust?).
So, by the process of elimination, it is not plastic tape, it is not duct tape, it is not friction tape and it don't stick well. Using a bit of logic, as the tape deterioriates over time and appears to have allowed moisture thru to the housing, it is most likely paper based. Masking tape has that type of property so as a replacment material, masking tape. Charles say grey or dark blotch. So the question remaining is - where do you get it?
Jim