Issue Picker Field does not support searching for EMPTY values

"Issue(s) picker" Script Fields do not support making comparisons and/or searching for null or EMPTY field values. For example, you are not able to make queries such as:

<Script-Field-Name> is not EMPTY 

<Script-Field-Name> != null

<Script-Field-Name> in ("")

<Script-Field-Name> in (null)

etc...

Trying any of the above can result in a number of different errors; the most prevalent being:

The field '<Script-Field-Name>' does not support searching for EMPTY values.

Steps to Reproduce:

• Create a new "Issue(s) picker" Script Field with only a basic configuration (just a field name will do) and ensure you've attached it to some screens in a local project for testing. 
• Navigate to the issue Search screen and make an advanced JQL query like:

<Script-Field-Name> != null

• Note the resulting error message:

The field '<Script-Field-Name>' does not support searching for EMPTY values.