This common duct tape tip is well known among backpackers. If wrap some duct tape around a water bottle or lighter you will always have a couple feet readily available for quick repairs.
In the video below I show some wrapped around a small disposable lighter, but taking the concept one step farther I took an old ink pin that was no longer serviceable and cut the ends off with a pipe cutter.
This left me a hollow tube as long as the roll of tape was wide.
I then wrapped about 4 feet of tape around the tube – in essence creating a mini-roll of black duct tape.
I then untied my monkey fist from my key-chain and threaded the tube along the length of paracord.
When I retied it, I now have a captive roll of tape that is always with me.
It takes no extra space, and adds very little weight.
I like it, and I hope it is useful to you. Until I went back to work at the prison and had to significantly alter what I carried in my pockets I carried this ring daily for years. Having the tape on your person leads you to have need for it more than you would think.