Here's how I've done it in 1:12 for standard clear sticky tape used in offices, with adjustments for 1:24 in square brackets.
You'll need a round toothpick, a knitting needle or a large safety pin the same diameter as the toothpick - approx. 1/12" across [1:24= use a heavy sewing pin, not the super skinny type used for lace or silk, a hat pin or medium size safety pin], sharp scissors, small ruler, craft knife and cutting mat, craft glue or a glue stick, a small scrap of paper from a paper grocery bag, lunch bag, brown envelope or regular printer paper if you want a white core, and an inch or so of the tape you want to miniaturise.
1) Prepare the core- From your paper, cut a strip 1/16" wide [1:32"] and about 1 1/2" long (which leaves you lots of room for handling). Take your round tool and starting at one end of your strip wrap it twice around the tool. Add the teensiest bit of glue to the strip right where you stopped wrapping to secure the second wrap to the first. When that has set a bit, wrapping 4 [2] more times for a total of 6 [4] rounds, adding glue every round. Cut off the extra paper and glue the end securely. Carefully slide the core up and down the tools a bit to make sure it hasn't stuck to it, then slide the core off gently and set aside to dry. (NOTE: If you are making a wider tape such as masking tape or packaging tape, adjust the core width as well as the tape width in step 2.)
2) Prepare the tape- While the glue finishes drying on the core, take your length of tape and press it to the palm of your hand 2 or 3 times to remove about half of the adhesive. It should still be somewhat tacky when you're done, but have have lost its' 'death grasp', making the next part easier. Find a clean, dry spot on your cutting mat (or make one if your looks like mine does) and stick the tape lightly to the board. Using the ruler to keep your cut straight, cut off a strip 1/16" [1/32"] wide from the long edge of the tape. (See note in Step 1 for making wider tapes.)
3) Assemble- By now your core should be dry, so all you have to do is carefully peel the strip of tape from the cutting mat and roll it evenly around the core. (I find it easiest to hold the core at both ends between my thumb and first finger, and use a combination of tweezers and fingers to place the tape straight and smooth it down onto the core.) Cut any excess off (and if necessary hold the cut end in place with a micro-drop of glue) when the roll is no more than 1/4" [1/8"] wide for clear sticky tape (Scotch tape) or 1/2" [1/4"] for masking tape, Duck tape etc... If you need a larger roll, just cut another strip and keep wrapping. The join won't show as it will be covered by the extras wraps, but the 2 strips be exactly the same width unless you want it to look like a roll of tape left in the rear window of the car all summer.
And if you're really into tape, get out some Fimo and a cut-off straight pin (for the spindle) and make a desk-style tape holder where the roll actually turns around. Just don't bake the holder with the spindle in the grooves of the holder, or you may never get it out to put the tape on. And don't ask me why I have five empty tape holders and five rolls of tape in a little baggie somewhere, or I may have a mini breakdown. :-D
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