I cant sign out of ebay for my wife to log in.

[redfive55]

When I try to sign out it just goes to " looks like this page is missing error message"

Here

https://www.ebay.com.au/n/error

And I dont get signed out

Using Google chrome

[imastawka]

It seems you're not the only one -

https://community.ebay.com.au/t5/Technical-Issues/Cannot-sign-out-of-eBay-on-Chrome/m-p/2319493#M466...

[andrew0123]

Im having the same problem. I'm also noticing a few other glitches that are becoming more prominent, including:

-Whenever I log out of one into the other it logs back into the original account. 

[meekamag2]

Yes. been doing it for weeks.

[nearly_invisible]

I'm having the same problem with Firefox, so it's not browser specific. A quick read of another thread suggests this glitch is confined to the Australia site.
What you could try to let you wife log in is to clear the browser cache and cookies, then exit and re-start Chrome.