Excel Autosave to local storage, how to enable this?

You can't.

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The new "autosave" feature that was forced onto your QAT ONLY works with OneDrive.
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If you want to create timestamped, or version numbered, "autosaves" to your local drive you will need to use an addon or macros.

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Autosave- Save the current document in two locations add-in for Word 2007 & 2010 and Excel
http://www.gmayor.com/SaveInTwoPlacesAddIn.htm
Originally conceived as part of the Save Numbered Versions add in, it was suggested by my friend and frequent collaborator Greg Maxey, that it would be better to retain its individual identity. I have therefore acceded to his suggestion and produced the add-in as a separate entity which does not require the presence of the Save Numbered Versions add-in, but will nevertheless work happily alongside it.
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Autosave
http://blogs.articulate.com/rapid-elearning/two-quick-time-saving-tips/
AutoSaver is a free application that autosaves files from applications you designate. You can download it here. Basically, you select your apps and then at what frequency you want to save. Or you can set it to autosave every app with some exceptions.
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autosave as macro in excel
https://answers.microsoft.com/en-us/msoffice/forum/msoffice_excel-msoffice_custom-mso_2007/auto-save-as-macro-in-excel/11bea4d6-d58e-48e2-b6cb-059f12a7ac23
I have written a code in excel that save as excel file in another location when user clicks save button.
ET MR Macros.docx.

Here is some general info about the MS Autosave feature

@ How AutoSave impacts add-ins and macros     01/01/2019
https://docs.microsoft.com/en-us/office/vba/library-reference/concepts/how-autosave-impacts-addins-and-macros
Learn about how AutoSave works in Excel, PowerPoint, and Word, and how it can impact add-ins or macros. When a file is hosted in the cloud (that is, OneDrive, OneDrive for Business, or SharePoint Online), AutoSave enables the user's edits to be saved automatically and continuously. When the file is shared with others, their changes are merged into this user's version of the file. If AutoSave is turned off, save must be triggered manually for the user's changes to be persisted in the cloud and for this user to receive others' changes. Currently, Excel, Word, and PowerPoint provide a BeforeSave event that allows a developer to execute code after the user triggers a save but before the save occurs. Excel also provides an AfterSave event that can execute macro or add-in code after the save completes.
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