Does the Eggplant integration allow on-demand script execution?

Yes, you do that in the Test Case 'Automation' section:

https://spiradoc.inflectra.com/RemoteLaunch-User-Guide/Eggplant/#setting-up-the-automated-test-cases

• Filename: This needs to consist of the following sections separated by a pipe (|) character:

  • The full path to the Eggplant command-line runner tool. To make this easier across different machines, you can use several constants for standard Windows locations:

    • [MyDocuments]: The user's "My Documents" folder
    • [CommonDocuments]: The Public Document's folder
    • [DesktopDirectory]: The user's Desktop folder
    • [ProgramFiles]: Translated to the Program Files directory. For 64-bit machines, it's the 64-bit directory
    • [ProgramFilesX86]: Translated to the 32-bit Program Files directory

  • The Eggplant Client Secret number and the Eggplant Client Id, separated by a comma (,)

  • The Eggplant instance URL to connect in

  • The Eggplant Test Configuration ID number to associate with this Spira Test Case

  • An example of filename would be: C:\Users\eggplant-runner-Windows-6.1.2-1.exe|umthdbvwiuy76bXStxzL,32584136987|https://mycompany.dai.eggplant.cloud|15d0d5e8-c3frt-8541-v5t9-d423760925f2

Yes, you can execute Eggplant tests on-demand from Spiratest, even if there isn't a direct field on the test case UI for it. This is typically done by associating the Eggplant test script name to a Spiratest test case's custom field (e.g., a field named "Automation Script Name"), and then configuring the Eggplant integration to look for and execute the script specified in that field upon an on-demand request.