The first and easiest answer is to remove the wheel covers and listen again for the clicking noise. It could be a pebble loose inside a wheel cover or a tire valve stem clicking against the wheel cover.
If it's not that easy, and your truck has CV joints, I would suspect a bad CV joint. Look for a torn CV boot.
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These answers by mechanics about dead batteries are amazing me. I am a girl...really into cars because I have had a few. I just had this problem in my 1989 classic Saab. The problem is your starter...The clicking sound means that the pin inside of the starter is not projecting itself and thats why when you turn your key you hear a clicking. Get your starter tested
If it makes a k-k-k-k-k-k sound, then it might be that the battery's dead.
Peterbilt is a truck brand. Pizza Hut is a brand.
A low or dead battery will have this effect. There is enough juice in the battery to activate the solenoid in the starter (causing the clicking sound), but not enough to turn over the engine. A jump start or a replacement battery may be needed if the battery is no longer capable of holding enough of a charge even when being jumped.
If the starter is clicking when you turn the key then the relay is not the problem, more likely is the battery and starter wire connections. Take them off and clean them before putting them back on ( have the battery checked ) corrosion will cause the symptom you described, however there should be a starter relay in the engine compartment fuse panel. If the truck is a standard transmission, it could be the Neutral safety switch, which is located under the clutch pedal. However, most likely it is the solenoid on the starter, I just had the same problem, time for a new starter.