I have a Sunpak DF4000U, is there a trigger that will work for this flash? I have been unable to find one that will work. I have a Canon 80D camera. Or does the trigger have to be specific to Canon rather than my Sunpak?
If you want to use the Sunpak DF4000U as an off-camera TTL flash with a Canon camera, you need either a wireless radio trigger set that is Canon E-TTL capable or a Canon E-TTL capable flash/optical controller that can act as a "Master" when attached to the camera's hot shoe.
The Sunpak DF4000U has a built in optical receiver that can pick up the optical pulsed light communication of a Canon "Master" flash, such as a 580EX II or a 600EX RT, an ST-E2 optical pulsed light transmitter, or the built-in flash of your Canon EOS 80D.
If the relatively weak built-in flash of the 80D is strong enough for your shooting scenario, you don't need anything else at all. Set the pop-up flash in the camera to be the Master (you can also tell it not to fire as a main flash, but only as the flash controller during the pre-flash sequences that occur an instant before the shutter is opened) and set the DF4000U to whatever the instructions call the "Canon E-TTL receive mode".
If you need more range, or to shoot in brighter light than the 80D's pop-up flash allows, you can use any Canon E-TTL compatible set of radio triggers to control the DF4000U off camera. In that case you need to set the flash just as if you are attaching it directly to the camera's hot shoe - the trigger receiver is essentially fooling the flash into thinking it is the camera, just as the transmitter is essentially fooling the camera that it is the flash. Please note that there are many different Canon E-TTL compatible wireless triggers available that all use their own proprietary radio communication protocol. You need to make sure your transmitter and receiver work using the same radio protocol so they can "speak" to each other in the same language.
An overview of the current Canon flash options can be seen on Canon's Europe website.
A word about why there are no 'Canon' or 'Nikon' versions of the Sunpak DF4000U:
The hot foot on the DF4000U has pins for both Canon's and Nikon's hot shoe contacts. The Canon system places the contacts in a different pattern than the Nikon system does. The DF4000U has both sets of pins and the same flash can be used with either Canon or Nikon cameras with full E-TTL functionality. Apparently the DF4000U also has the capability of using its optical receiver to receive either Nikon or Canon wireless optical pulsed light signals.
Following up on Michael C's answer above I found that the DF400U works off-camera in Manual S1 and S2 slave mode with my Nikon D7000 using optical synchronisation. I just pop open the built-in flash atop the Nikon and it fires the Sunpak DF400U slave flash.
I am still trying to decipher the manual. It really needs to be rewritten in better technical English. Otherwise the flash works well and is amazing value.