I'm not sure how I've never noticed this before, but it looks like the Print Widget is not able to print the basemaps, which are sourced from Arcgisonline. All of our other layers will print, just not the online basemaps.
Everything is sourced locally from our internal AGS servers, except for the basemaps. The printing geoprocess is also on our local AGS server.
The map has no problem displaying the basemap, just unable to print it out. The AGS server log is as follows:
Error executing tool. Export Web Map Task : Failed to create layer from service at https://services.arcgisonline.com/arcgis/rest/services/Elevation/World_Hillshade/MapServer. Failed to execute (Export Web Map). Failed to execute (Export Web Map Task).