- Create a new issue picker script field and assign empty JQL query on it.
- Click configure contexts and add a new context.
- Click "Modify field parameters here" to change the JQL query.
- Go back to the old context and its override the JQL query.
Replicate on JIRA Software 8.10.0 and ScriptRunner 6.5.0-p5
Each context should have its own JQL query without override each other.