Ok you need this relay:
Radio Shack. Should be available in stores. You might have to call around a few RS stores. The price is $4
275-248
10A SPDT contacts and 12V coil.
Polarity doesn't matter on 12V side.
For the contacts, you'll see three terminals. Common, normally off and normally on.
Normally off means it's off when the power is off and turns on when power is applied. Normally on behaves just the opposite.
First, you need to cut a 120V cord. Pull the covering off the wires. The white cord or if not color corded, the one that leads to left side(ground pin facing down)/larger prong connects directly to your load. The black cord from power goes to common and load black connects to normally off terminal. Leave the third pin unused.
That's it.
Don't even bother with solid state. They wreak havoc if your load doesn't meet the requirement. (minimum load, maximum peak current and many other factors)