Title explains it - I have created a simple widget which is a button that opens a modal for users to login and receive data from an external API. How would I add this button somewhere on the incident form?
Record Producer from the service catalog are displayed in "service portal" -> "pages" -> "sc_cat_item". On this page you can add your widget. Since all record producer and catalog items are displayed in this way, your widget will show up on all of these items.
If you want to show the widget only on one particular catalog item (your incident form), you would have to add a ng-if to the new simple widget. Something like ng-if="data.sys_id == idOfSimpleWidget"