This shows how to hook up a relay to use a fogger timer to run something of higher power. Eliminate the relay and wires going to the relay on this drawing for your purpose. You need to get insed the timer for what you want to do (and jumper the "fog" switch).
For myself, I modified a fogger timer with a relay to close the "fog" button when I pushed a "low voltage" button.
The schematic shows whats going on inside the fogger and inside the timer so you know where to jumper your relay into.
If you need more help...I can explain more.