re: Transistor or relay?

One more:

Go to Lowes / Home Depot. Buy a cheap outdoor motion sense light. Remove the motion sense unit from the light. Wire it to your power for the smoke machine. Set the sensitivity and on time as you would if you were setting up the motion sense light.

You could even go crazy and mount it in a workbox with an outlet you could use to plug other things you want motion sense to work with. Then you don't even have to cut the cord on the smoke machine.

Just make sure it is not one of the LED motion sense lights. And as always, don't exceed the wattage the original fixture or the motion sense unit is rated at.