How to prevent profile pages from revealing when I was last online on steam?

I always start my steam with "Automatically sign into Friends when I start Steam" disabled.

It seems to work — people can't see if I'm online. But when I check the profiles of my steam buddies, there I can find myself and the time when I was "Online last time".

There the last time is always set to the time when I logged into my account. I don't like it — how to disable this?

Make your Profile Private so that they can't access to your Profile. If you do so, they won't be able to see when you were online, but on the downside, they can't see anything.

To get around this, I created another Steam account, and added it as a "family" account so I could share the game library of my regular account.

When I want to be anonymous, I log into the new account. If I want to be available for my friends etc, I log into the original account.

This is not possible to change.