I know this is an older post but I thought I would share my experience and hopefully help someone looking through these older posts.

I have very oily skin and have had a horrible time with tapes. They all break down to a gooey disgusting mess within a week but I have finally found the solution.

this is a two-part fix; 1. USE RED LINER TAPE BELOW YOUR REGULAR TAPE! I have no idea why this works so well but it does and I can not recommend it enough. for whatever reason, the red liner tape does not break down like normal tape will, and using it kind of acts as a barrier to your regular tape and protects it. Not only that but it makes clean up a breeze.
2. The best tape I have found is Sunshine Stick-it tape. it does not break down near as bad as all other tapes I have tried. Stick-it tape + the red liner tape is the bomb! I can get 2 weeks with a strong bond and almost no lifting.

Now glues are a different story, I have tried multiple and still have not found anything great. the best so far has been ghost bond platinum but its far from perfect. I recommend you stay away from any clear bonds tho because they break down and go through the base and into the hair. it's a horrible mess.