quote: "Suppose I have a trade secret and some big pickup company buys my product, takes it apart and starts using my idea?"

Unless they stole the secret somehow, tough luck. Reverse engineering is allowed, unless some law specifically forbids it. To protect an idea without secrecy requires a patent.  
 
The only area I know of where reverse engineering is forbidden by law is content protection schemes covered by the Digital Millenium Act, but this does not include guitar pickups.