When you want something to pop out, you gotta have layers.  In order to do that while keeping the object stuck on the card's surface, I suggest you use foamed double-sided tape.  I don't quite know how it's called back home since I didn't discover this stuff until I came to Taiwan, but all it is is a thin piece of foam that acts as double-sided tape.  It secures the object while giving it a layered look.  If you want something to pop out even further, add another layer of tape to it.  Not only does the tape make things stand out, it also sticks really well.  Although, a downside to any kind of double-sided tape is that once you make a mistake, it's hard to correct.  In other words, once you stick it down, you can move it without damaging the surface. 
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