A couple of notes.
On WS2012, the WSUS console is a "feature", and you'll find it listed under Features -> Role Administration Tools. (See below).
Knowing unequivocally that installing WDS would not remove WSUS, nor can you remove a role using the "Add Roles and Features Wizard", it does beg the questions of WSUS apparently became uninstalled from this server. I would suggest combing through Event Logs for anything relevant to that purpose.
Uninstalling/reinstalling Patch Manager is not going to be able to fix a broken WSUS installation; more to the point, the only thing that would be required is to just fix the broken WSUS installation.
However, now, you also have a broken Patch Manager installation.
If there's nothing else running on this server except WSUS (broken) and Patch Manager (broken), and you've not actually implemented anything with WDS yet, you might just consider blowing it all away and starting from scratch.
Or, if WDS is already configured, or if you don't want to reinstall the OS, clean up the role installations for WSUS, verify all components are removed (e.g. IIS v-dirs, registry keys, %ProgramFiles%\Update Services folder), verify the WID really has been removed. Reboot the server and re-run the PM installation. (If the WSUS server is fully cleaned up, the PM install should be able to build a new WSUS.)
Or (safer, but more work)... install the WSUS role on the server without using Patch Manager. Verify that the WSUS role is installed and functioning, and then install Patch Manager using the "Advanced Installation" option, where it will give you an opportunity to tell it to use an existing WSUS Server.
