Thanks for the replies. I tried staying on 12.x with updates disabled, but it was annoying me with frequent popups in relation to module updates unable to be installed.
But the good news is that I seem to have been able to solve connectivity with EIS 13.x using Pulse Secure.
What I had to do was:
Advanced Setup > Detection Engine > Real-time file system protection > [Disable] Enable Real-time file system protection
Advanced Setup > Network Protection > Firewall > Basic > [Disable] Enable Firewall
Right click EIS taskbar icon and select "Pause Protection"
Now I can connect to my company vpn under 13.x.
I noticed if I perform the above steps out of sequence, i.e. step 3 before step 1 or 2, it does not work. I need to perform step 3 at the very end. I am not sure why. Maybe pausing protection, then disabling the firewall and real-time file system protection doesn't shut down certain modules correctly. I am also not sure why I have to do step 1 even if I do step 3, because doing step 3 tells me it is deactivating real-time protection anyways, which is confusing:
So doing steps 2 and 3 alone will not work... confusing... But anyways, I got it working now and I am happy.
Thanks again for all your help.