I once did a real quick emergency fix on a leaky tank with Blueskin.
Blueskin is a construction membrane make for waterproofing around windows, doors and such during the home building phase.
It has a 100% waterproof membrane on one side, and a VERY sticky, tar like adhesive on the other. Sticks to anything and everything, as long as it is dry and semi clean. Comes in rolls in various widths. And it is always very flexible, allowing for expansion and contraction.
I was on the road for a couple weeks when I found the leak. I happened to have a roll of the stuff with me so I did the fix right there.
It held so well, it was still there when I sold the unit.
There are a pile of different manufacturers of similar products. Bakor Blueskin is just one of them. I buy it at the local lumber yard where home construction materials can be bought. Might even find something similar at Home Depot.
Forget the duct tape, that will never hold.