What is the width of the tape? One inch wide tape obviously has 1/3 more strength and stickiness than 3/4 inch, the most common.
I use packaging tape, the kind with fiberglass in it. It can't be broken and the adhesive is very strong but not gooey.
Of course, taping new film to an old film "trailer" is nowhere near as reliable as taping the film, over the core, and then again on the film's other side.