Here is the Release bearing (aka Throw Out Bearing) and the crack is clearly visible.
Here is the Pilot Shaft that is aluminum and press-fit into the Bell Housing. The yellow residue is Toyota spray on Lithium White Grease and was a bad idea as my technician could have contaminated the clutch disk and or flywheel.
Here is the Release Bearing positioned on the Pilot Shaft:
Here are 2 views through the cover plate. When the clutch pedal is depressed, the Release Bearing will move forward less than an inch, and return to the at rest position when the clutch pedal is released. The Release Bearing is in constant contact with the Pressure Plate fingers and thus the Release Bearing is spinning at all times. We have speculated that the loose fit (from the crack) of this steel on aluminum design, combined with the forces of the Pressure Plate fingers and the pivot of the clutch fork (not shown) causes the Release Bearing to grind and wear various areas of the Pilot Shaft. Once diagnosed, the technicians felt confident that a new Release Bearing would solve the issue. Since it makes good sense to replace the pressure plate and clutch disk and perform a runout test on the flywheel when replacing a Release Bearing, I ended up paying for all of that too. But once detrimental damage occurs to the Pilot Shaft, a new Release Bearing no longer corrects the chirping noise and it returns quickly, as in my case. The only option is to replace the Bell Housing or drop a brand new transmission in the truck. I went the Bell Housing route due to costs but the tranny was never the same afterwards. I only paid for the parts since I already paid the labor once and the Pilot Shaft wasn't properly inspected.
When viewing the operation of the Release Bearing with the engine running and the cover removed, the technician should be able to demonstrate the wobble using a flashlight. Applying a small amount of pressure to the slave cylinder shaft which moves the Fork, should stablize the Release Bearing enough to stop the chirp. That is the fastest way to diagnose this issue. The next step is to drop the tranny and while it is on the bench, a detailed inspection of the Pilot Shaft is required to confirm the diameter is within tolerance otherwise the repair may not last very long.
IMO, acting very quickly to the chirping sound may avert detrimental damage to the Pilot Shaft and keep your repair reasonable (if denied warranty) by limiting the repair to the replacment of the Pressure Plate, Release bearing and Clutch Disk components. Note that the 4 cyl 5-speed 05+ Tacoma manual transmission (R155 and R155F) has a superior design because the Pilot Shaft is a replaceable bolt-on component to the Bell Housing. The FJ Cruiser 6-speed manual trasnmission (RA61 and RA61F) is of similar design to the 05+ Tacoma 6-speed manual transmission (RA60 and RA60F.)
Lastly, I specifically insisted that I keep all of the old components (evidence) before the work started and I would recommend that any of you working on similar issues insist that you receive the old components.