Are you 100% sure it is a relay? Even the manual climate system uses an electrically operated blend door to control air temp out the various vents based on the temp dial position. If the cheap plastic gears inside the blend door activator strip, you will get a click sound every few seconds as the motor tries to move the blend door to the comanded position. Try turning the temp control to warm or cool and see if the noise changes or stops.
05 Taurus SEL Duratec - my daily driver
04 Taurus SES Duratec - wifes car
95 Taurus GL Vulcan winter car
Toy #1 - 86 Tbird 5.0 (original owner) - LOTS of mods
Toy #2 - 88 Tbird Turbo Coupe - LOTS of mods
02 Pontiac Grand Prix GT
67 Honda 450 Super Sport - completely customized