Thank you all for the replies. That looks like it would work, but I ran into a couple of problems.
First, all I have out there are three wires, the two 110V legs and a ground. Secondly, burying new wire to make another circuit with a neutral wire would be no easy feat. The well is on the opposite side of my house than the panel box. Even if I could go through the attic to the other side of the house and down that wall with the wire, between that point and the well I have electric, main water lines, sprinkler irrigation lines, and four-inch corrugated pipe that drains my gutters to the front yard. That's a lot of stuff to miss and go under with the electric and I don't know where some of that is. If I were to take it from the panel box around the back yard and over to the well, that's a lot of digging and missing the septic system on that side.
Disclosure: In my posts I say I do this and do that, but it's not me actually doing the work. I suffered a spinal cord injury 16 years ago that left me a quadriplegic so it's my dad who helps me with all this stuff. The more I'm thinking about this, the more I'm wondering if there is an easier way to control the well pump in the event of an emergency (a pipe breaking). I was just hoping I could pull it off with the existing wiring that's already out there and control it with INSTEON. INSTEON just gives everything that "cool factor".