2001 Ford F-150 Trouble starting

In the fall, the electric fuel pump does not always come on when I turn the key to start. Truck sits in a garage 6 days a week. If pump comes on, truck starts. I have to turn key off, try again until I hear the pump come on, then truck starts and runs fine. Outside of garage, I can't always hear like I can in the garage. I changed the fuel filter, and still have the issue, especially when the weather changes. Is there a bad relay or is it in the ignition?