The relay switch has a fine wire coil inside which is perfect for a pickup. Combined with a strong magnet it can produce a really good sound.
This pickup only works for one string. However, if you want to use it for multiple strings, you can combine multiple pickups to create one larger unit.
Step 1: Parts
PCB relay switch: I found the relay I used on an old circuit board. Look around first! You can find them on plenty of circuit boards that are being thrown away.
1/4" mono audio jack: You can pick these up pretty cheaply at most electronic stores (Maplin/RadioShack). Also check out eBay. I bought 3 or 4 for about a fiver.
Wire: Any thin wire will do really.
A small strong magnet: As strong as you can find. The stronger it is the louder the output!!
In the first picture above you can see inside the relay. The left side of the relay is the part we're interested in, the coil. This will be the main part of our pickup.
The second picture shows what most relays will look like on the board.