Strange issue with Windows Update occurred. In this case Windows Server 2012 R2 was trying to install 2 updates for Office 2010 but was failing.
KB4461579 failed with Code 780
KB2553332 failed with Code 780
First it turned out that a 64-bit version of Microsoft Access database engine 2010 had managed to get installed which does not play nice with 32-bit versions of MS Office on the same machine. The 64-bit engine was uninstalled and then replaced with the 32-bit version. When the 64-bit version was uninstalled, it also removed the 64-bit version of the Office Source Engine service from the system that was showing up in services.msc. However after this change, the 2 Windows updates listed above were still failing.
Also installed on the system was Microsoft Access 2010 Runtime. Within Programs and Features of the Control Panel, performing a Change->Repair option on it completed fine, but wanted a reboot. After rebooting, the two Windows updates listed above were then able to complete successfully.