Whirring/Rubbing Noise After Ignition

I recently noticed a strange whirring/rubbing sound coming from my engine after ignition. Here are the symptoms:

2008 Tacoma TRD V6 110K

A/C Fan On
Turn Ignition
Engine Turns Over
A few seconds later you can hear an audible whirring/rubbing noise which wasn't there before. It almost sounds like an electrical motor trying to engage.
It only lasts for a second or two and then goes away. I have only been able to replicate it once, directly after the first time I heard it. So, far I have heard it three times now, even after multiples attempts at replication.

Attempts at Resolution:
The first time I noticed this, I thought it might be the starter not getting enough juice from the battery. So, I checked my battery terminals, and they were badly corroded. The corrosion (on the terminals) has been cleaned off with felt pads and dielectric gel applied. I have not had time to replace the cable connections. I also had the battery checked and it is pumping out more CCAs then it is rated for.

Second, last year, I noticed that the engine would idle kind of rough when the A/C was on. It is noticeably smoother when the A/C fan is off. Wondering if the whirring noise could be related to the A/C kicking on..Or, something bigger like the starter or transmission.

I'm having it looked at on Friday. But, was just wondering if anyone has experienced anything similar.

 

I've noticed the same thing on my '12 DCSB V6. Almost sounds like something's pulling a vacuum and then stops. Don't know if that's what you're describing. I'm curious as well as to what it might be.