I would love to make a puppet that has electronics embedded in it.
Two materials that I found are used to make puppets and action figures are PLIABLE WIRES and MODELING CLAY.
The wire has to be strong but pliable. I believe that there are different metals available for these wires, and depending on the use of the wires I could get conductive or non-conductive ones. Here's a link for one type of wire that is sold at Omer DeSerres:
There is a modeling clay that comes in different colors called FIMO, however, I think that if I want to make a complex and solid model, I should get this special clay used for modeling, it is called Super Sculpy. It is quite soft but becomes rock solid when baked in the oven. It can contain wiring inside and electronic parts can be embedded in it.
What the project with those two things could be is making like a toy that could react to it's position and interact with the user through computer messages or sounds according to how it's being manipulated.
However, for the Switch project, I'd make something simple like a lamp, where, for example, if the character has it's hands touching (and the switch is activated), lights embedded in his body turn on. The toy can have more than one part, which means I could make like a centipede and have to have all the parts of the centipede touch together in order to have the connection and the lights working properly.
Another material that I discovered by searching paints was this carbon paint, which is conductive as well.
I suppose it could be applied on most surfaces but could crack on bendable ones, so I guess it should only be applied to hard materials.
Other materials that I know and am interested in but I've never used are plexiglas and conductive thread.