Can't Get ACR Updates for PS CS6

Question

My computer is a PC with Windows 7 Home Premium 64-bit with 8GB of memory.  My problem is I don't seem to be able to get any of the Adobe Camera Raw updates for Photoshop CS6 (perpetual license).  It's stuck at ACR 8.1.  I also can't get the last update to the PS CS6 application (13.0.1.3).  As you can see from the screen capture of Adobe Creative Cloud desktop application, it says I have Photoshop CC and Photoshop CS6 and says all applications are up to date.  This is not the case as I have stated above.  ACR should be at 8.4 and it's at 8.1.
If I open PS CS6 and go to Help > Updates... I get the message that all applications are up to date.
If I click on Preferences, it says "Only show updates for the following products" and there are no options to show updates for any CS6 products.  Again, this display came from the Help menu in PS CS6.  Why doesn't it show an option to check for updates to CS6?  My PS CS6 application was a perpetual license purchase and wasn't converted to a Creative Cloud application.
I have been following several threads at this forum and the Photoshop forum that discuss problems similar to mine but have not found a solution.  I followed a link in one of the responses to a download for ACR 8.4 for PS CS6 on Windows and thought I could do a manual installation.  Instead, I got the following message that the update failed because "This patch is not applicable to you."  I got the same message when I tried to manually install the Photoshop CS6 update to 13.0.1.3.
I would like to keep my PS CS6 (perpetual license) up to date, but I don't know what to do now and am hopeful someone in this community can help me with this issue.
Thanks,
Chas

Answer 1

Thank you very much, ssprengel, for this very helpful information.  It never occurred to me that the camera and lens information was stored in a common location shared by both CC and CS6.  Also, thanks again to Michelle for her useful reply as I did not know that the same ACR file could be used for both PS CC and PS CS6.
Although, I still don't know why my PS CS6 won't update properly or why the manual installers refused to run, you two have provided a satisfactory work around to keep ACR for CS6 up to date.
I'm sorry I can only mark one answer as correct and both you and Michelle's answers were very helpful.  I marked Michelle's reply as correct because it let me know that I could copy the CC ACR file into the correct CS6 folder.
Thanks,
Chuck