Several ways a fan clutch can fail. As above codes can set. Dropped dead failures, leaks, locked up bearings, open wires, shorts are clearly an INOP fan clutch and easy to diagnose.
The concern is a old lazy weak clutch (A survivor that didn't die from the above clear cut failures.) that can't respond fast enough to keep the AC system from extreme high side pressure spikes. As explained elsewhere most of the 2003-2007 5.9's do not have any "code" to shut off the compressor IF the high side is overheating and experiencing extreme pressure over 450 Psig due to a fan clutch that isn't kicking on fast enough. These trucks blew the AC relief randomly when brand new. So it's hard to see through the symptoms.
The engine and cooling system are a huge heat sink vs. the heat capacity of the small AC condenser. So the engine temp is the last to start to rise as a fan clutch wears out, but, the AC system has already suffered badly. Anything over 45 MPH and the fan isn't needed at all for AC. At idle is where the AC will fail on a weak fan clutch.
In my case the idle fan RPM was below 600 RPM measured at the fan on a cold day when the AC or ECT did not require any fan. I recall it was around 400 RPM. IMO this RPM is too low for the fan clutch to get the working fluid moving as well as internal wear and fluid wear out. Kicking the AC on resulted in a very slow RPM change while the AC high side ran away over 400 Psig. A new fan clutch was holding around 600+ Fan RPM when not being called to run. An optical tach or trained eye can see this low RPM. Never set a code, but, vented the AC 4+ times it's last year.
Geno's Garage "tool free" advice is similar to: If you start the truck and the fan isn't roaring from morning sickness: turn the AC on with blower on high. The fan should be running in a block or so at 25 MPH. If you start the truck, AC off, and the fan is roaring from the normal morning sickness: simply wait till the fan kicks out in a few min. Then same kick AC on, blower on high, and again it should be roaring within a block. Assumed somewhat of a summer day.
The obsolete spring thermal clutches are the same technology in the "clutch" part of the fan: only the control has been replaced from a thermal spring to a electric valve controlled by the ECM. The ECM can compensate some for RPM lost due to age. However there are limits when the ECM is asking for 100% and time to get there is excessive, but, not tripping a code. Is the fan clutch under your hood over 5 years old? Yes? Then you are not throwing parts at it. I have not seen an age/miles recommendation rather an age only recommendation for fan clutches in general and NOT specific to our fan clutches. Again the underlying technology that fails due to age is the same as the old clutches that have a recommended 5 year life. 5 year life is because they loose 200 RPM per year so 5 years is 1000 RPM lost.
I recall the factory manual has a 15 min test. Bluntly at idle with the AC blower on high the system will dump the R134a out relief valve before the 15 min "It's dead Jim" test will show a INOP fan clutch.
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