There are any number of free VNC clients for Windows. For years now, I have relied exclusively on TightVNC.
What I am trying to do is to control the remote computer / desktop so
that the person that sits in front of the computer can see what I am
doing (mouse movements, windows, typing, etc.).
Yup, TightVNC will do that - a ghost at the controls, as far as the bewildered user is concerned.
Plus you can use it to replace x11vnc on Linux
TightVNC is a free remote control software package. With TightVNC, you
can see the desktop of a remote machine and control it with your local
mouse and keyboard, just like you would do it sitting in the front of
that computer. TightVNC is:
free for both personal and commercial usage, with full source code available,
useful in administration, tech support, education, and for many other purposes,
cross-platform, available for Windows and Unix, with Java client included,
compatible with standard VNC software, conforming to RFB protocol specifications.
With TightVNC, you can:
cut your expenses and save your time on traveling,
help your friends and family to solve problems with their computers remotely,
make sure nothing wrong is happening on your computers when you are away.