Amy Roust
unfortunately you are running into a bug where print service fails to draw a feature layer when its default visibility is False in the map/feature service.
good news is that this is fixed in 10.7.
until you migrate to 10.7, you can go with one of the following options:
1. make the Parcel layer visible in your map and republish the map service
2. add your service as a mapImage layer (aka dynamic map service layer where the url ends with '/MapServer') instead of a feature layer (where url ends with '/MapServer/<id>')
hope this helps.