This process will automatically generate a separate document for the gift message to print.
Step 1 - Label Template
Setup a word label template:
Type = Additional Document
Name = can be anything, but whatever you use needs match the param on the order rule exactly e.g "Gift Message Doc"
The document contains either Item or order level gift message:
Step 2 - Order Rule
Generate Additional Document = this is for order level gift messages
Generate Additional Gift Document = this is for item level gift messages
Param = this is the document name you used for the label (Gift Message Doc)
Gift Messages with Operator set to "Empty" or "Not Equal"
You may need to generate multiple rules with both condition types set depending on the channels in use and gift message mapping type (order level / line level)