I called 3M and spoke with someone that narrowed my search to two types of tape, they sent the data sheets for the products and sent a sample of each . The problem with some electrical tape is a chemical reaction between the adhesive and the tape. Over time, the adhesive separates form the tape and the bond fails. What's left is a gooey mess. I have also used Duct tape, it's a lot stickier and more difficult to re position.
OK lets build a kaleidoscope.
First cut three strips of mirror. I think you should use inexpensive mirror like mirror tiles for your first scope. OK, cut three stripes of mirror. Now, using black electrical tape, place 3 strips of tape about 1 inch long across one edge of each of the mirror strips. Next, take the two wide strips, and stand then on end on the table top.