Windows 10 – How to Show Weekday in Taskbar Clock

Unfortunately the answer is no - And this is also the same on Windows Vista and Windows 7.

The reason for this is that they are displayed by the Explorer process and unless the application safely quits, it sends no notification to Explorer about disposing the icon.

Short of closing and reopening explorer itself, I am not sure of anyway to accomplish this. I am guessing that it would technically be possible as I remember using a program called Dohide years ago when I was at school that hides running processes. But this was simply hiding, it did not detect and close running ones...

... Anyway, I have never come across any application that does it. Quite frankly, if an application does crash, the manufacturer / developer should really go about fixing it, and running your mouse over the icon does fix the problem, so I am guessing no one has thought that it would be worth creating an application or way round this.

This is not currently possible without using third party apps. While windows allows you to change the short-form and long-form of your default times (Control Panel -> Region and Language -> Additional Settings -> Time -> Short: hh:mm:ss tt), this change does not take effect on the taskbar clock.

As @CharlieRB noted, you can use the Clock gadget to display the clock on your desktop, or you can click on the time to see an expanded calendar/clock flyout with the time in seconds.