It's Hair Loss Support At Its Best
Have you considered a water soluble adhesive to attach your wig rather than tape?
There are daily application water soluble adhesives that might work well for you like Tensive Gel, It Stays, and Gotta Be Glued. You can likely find them all on Amazon. Got to Be Glued is sold in most grocery stores, pharmacies, Target, and Walmart. They can be easily removed daily with water. You might want to experiment with each one to see which provides you with the most secure hold.
You might also want to have an elastic band sewn into your wig to provide even more of a grip. There are also Wig Grips like StarShemya and Hagster mentioned but they don't work for everyone. Clips are another good option but they can take some getting used to and need to be moved regularly to avoid traction alopecia.
Hope that helps. You'll find a method that works well for you with some experimenting. :-)