Script trigger can be executed on any field on a layout. Test it with the debugger and see if you're sending the right parameters.
And which trigger are you talking about? In some cases you need two triggers for one action: one to store the current contents of the field and one to do what you ant to do.
agnes b. riley
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Script triggers are invoked by direct operations only. Clicking in/out of a field is a direct operation. Changing a field's contents via a script or calculation via relationship is an indirect operation; therefore script triggers are not executed. (Neither are they executed when performing bulk operations - Import, Replace, Relookup, and in most cases, spell-check operations.)
Agnes is correct in that the field must reside on a layout and that field must be directly operated upon for the trigger to execute. Perhaps you could give us a few specifics on exactly how you're trying to trigger the script; is it when you are actually in the related field? Is it via a calc? Via another script?