How do I use a Wacom Intuos 3 with OS X Mojave (10.14.5)?
The Accessibility options seem to be key, initially. From Wacom Intuos 3 Tablet Issues with Mojave OS. Does the CTL4100 work?


  Go to System Preferences / Security and Privacy / Privacy Tab / Accessibility / click the lock in the bottom left corner of your window to unlock (you'll need your password), then you can select the Wacom tablet in there. I just had the same problem and this worked great for me. Hope it works for you!


In addition, there seem to be some additional steps requried to obtain full functionality. This thread on Reddit, Solution for Intuos 3 PTZ-630 in macOS 10.14 Mojave, seems to have a fuller solution:


  Need to make sure you go to
  
  System Preferences >> Security and Privacy >> Privacy >> Accessibility
  
  and make sure that Photoshop and WacomTabletSpringboard are both added
  AND checked on the right panel.
  
  ...
  
  My process (for what it's worth).
  
  
  already had driver 6.3.15-3. Clicks not registered. Tablet    diagnostics say everything is good.
  uninstalled driver redownloaded 6.3.15-3 and reinstalled.
  didn't work. Uninstalled 6.3.15-3
  reinstalled older 6.3.14-2. Didn't work. Uninstalled.
  installed latest driver, 6.3.31-4 (definitely NOT for Intuos 3).    Didn't work. Uninstalled.
  reinstalled 6.3.15-3. Didn't work.
  found out about having to enable apps (WacomTabletSpringboard and    Photoshop) in the accessibility options. EUREKA! clicks now
  registering, but Photoshop still with no pressure.
  checked other graphic apps. Pressure recognised. Hmmmm.
  leave Photoshop pretty much alone for a day, pressure now working.
  


also, in the same thread:


  After several fresh installs and restarts, i realized that there was a
  new button towards the bottom right in Security &amp; Privacy > General
  
  it was saying something along the lines of some stuff did not load on
  restart. Button was labelled Allow
  
  I tapped on it and a dialog box that had two items in itpopped up, one
  wacom and another one that was probably wacom related, i hit allow and
  my pen's tap to click started functioning again. Cheers.