>>>I did try to restart the service and all works fine. So, in my opinion, stopping/pausing/restarting the service is not what I am looking for. I need to be able to set something to have the connection time out. But maybe such thing does not even exist.
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>>You'd need another box, with SQL server on it, express version would suffice. It may be virtual. And then you just yank the network cable (simulate network breakup), or suspend that machine (server down - works the same with virtual), or go for a walk and see if it timed out on you when you come back.
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>I do have another PC, Windows 10, which is on the same "network" since both PCs are working through the same router. I need to re-learn how to be able to "view" the Windows 10 from this, Windows 7.

Good luck. I think on the machine where you put the SQL you only need to open port 1433 both ways (in and out) in the firewall settings. I did that on a few 2012 or 2016 servers (perhaps ever newer ones) when the customers had partially installed the SQL server, leaving everything on default. And we know this server is written by the world champion in the category of wrong defaults. Sometimes I think they add a feature only in order to annoy us, so we'd have to find where it's set (or more often tamed, disabled or just shot). So I sort of remember what the usual steps were: enable direct logins (default is to use windows/domain logins), change collation to that of the country (specially if the server is in Slovakia and the owners from Canada, they'd never remember to set this)... and then fiddle with the rest if annoying, this alone should be enough to make it work.