Hi CodingMann,
>>When I click on the "Prerequisites" button in Visual Studio, it lists SQL Server 2008 Express, but not the 2012 version.
Because the version of your Visual Studio 2010 is lower than SQL Server 2012, it does not include the SQL 2012 by default, you can add the package by yourself.
>>Now, I need to know how to include SQL Server 2012 Express SP3 as a Prerequisite in a Visual Studio 2010 ClickOnce deployment
Please refer to the following documents to create Bootstrapper Packages:
Creating Bootstrapper Packages.
How to: Include Prerequisites with a ClickOnce Application.
Also I upload a package to Microsoft OneDrive, try to download it and decompress it, then put it to the following folder in your computer:
C:\Program Files (x86)\Microsoft SDKs\ClickOnce Bootstrapper\Packages
Package: SQL Server 2012 package.
In fact, the most convenient way is update your Visual Studio to 2017 version, this version includes SQL Server 2012 in the Prerequisites by default.
Best Regards,
Stanly
MSDN Community Support
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