How would I go about repairing this leak?

Switches are cheap. If you are comfortable with doing a little electrical work, then it's simple. Turn off the power at the breaker, undo the wires, being careful to note which one goes where, unscrew the switch from the little pipe leading to the switch, replace the little pipe if needed, screw new switch on using plumber's Teflon tape, replace wires in the same order that they were on the old switch, and turn the power back on.

You will need to be aware that switches come in different pressure intervals. Some cut on at 20# and off at 40# (20/40), while others are 30/50 or 40/60. You can see that selection here.

Wayne Water Systems 30-50 PSI, 0.25" Pipe Tap Square D Pressure Switch - 66021-WYN1 | StudentMarket.com, Inc.

This site gives a nice description of how to replace the switch.

How to Replace a Water Pump Pressure Control - private pump and well system do-it-yourself repairs