How to connect primer tubing to non-laundry faucet?
Another option would be to install a flow-through trap primer.  This is a device that feeds a small amount of water to the trap primer everytime the supply it is connected to runs.  One constraint is that it needs to be oriented correctly due to the air gap.

The one pictured is from Watts


  Series A200 Flow-Through Trap Primers are used in commercial and residential applications to assure delivery of water to floor drain traps to prevent the evaporation of the water seal that protects a building or room from sewer gas fumes. It consists of a bronze body construction with a Celcon seat and disc. Available in threaded (Model A200) or union solder (Model A200S) connections. Minimum Supply Pressure: must exceed 25psi (172kPa), Maximum Supply Pressure: 125psi (8.6 bar).