The work-around mentioned in the link above to sudo apt-mark manual python-gnome2 will not work for 19.10 because that package does not exist in the ubuntu repo :(
Forcing the deps with --force-depends does not work for the same reason, python-gnome2 does not exist.
This is worked on my Ubuntu 19.10 Desktop...YMMV
Step 1 (prerequisites)
Make sure you have these packages installed
sudo apt install python # installs python2.7
sudo apt install python-gtk2 # used by the GUI
sudo apt install equivs # improvement by @Chemary, Tx!
Step 2 (create control file)
Now we need to trick Ubuntu into thinking it has python-gnome2. To do this we will use "equivs". Lot's of good docs on it, but here's a brief rundown:
equivs-control python-gnome2
This creates a DEB control file called python-gnome2 (see example below) in the current directory that you will need to edit. Or you can use this one...feel free to put in your own name/email and stuff...leave everything else
Step 3 (edit control file)
Using any text editor change the created control file like this. It will be in your current directory (assuming your working from the terminal) and will be called python-gnome2
Section: misc
Priority: optional
Standards-Version: 3.9.2
Package: python-gnome2
Version: 1:42
Maintainer: Jack Ford <mike@clustergarage.io>
Architecture: all
Description: A fake package to make FAHControl install
Step 4 (build a fake package)
Then build a fake package with the control file you just edited
equivs-build python-gnome2
This will create a DEB package in the current directory called python-gnome2_42_all.deb ...assuming your control file looks like the sample above.
Step 5 (install)
Now you can install your fake package and fahcontrol successfully and your Apt tree will not be broken. Run these commands from the current directory.
sudo dpkg -i ./python-gnome2_*_all.deb # improvement by @Chemary, Tx!
sudo dpkg -i ./fahcontrol_7.5.1-1_all.deb
Note: If you downloaded fahcontrol_7.5.1-1_all.deb file to say your Downloads directory, then you would need to install it from there e.g.
sudo dpkg -i ~/Downloads/fahcontrol_7.5.1-1_all.deb
Step 6 (save the world!)
Then run it like this from the terminal
FAHControl
Or use from your application launcher. Mine looks like this

Hope that helps!