Layout Mode UI is not consistent when it comes to assigning script triggers to a button. Button objects offer a way to see and select triggers. You cannot do this with grouped objects that have been formatted as a button.
See this discussion for a lot of detail on the subject: How do two trigger script icons happen to appear on a single field?
To reproduce, put a button object on your layout and right click. You get a sub menu that includes the option to set a trigger. Now select a field and use button set up to turn it into a grouped object button. Right click it and there's no such sub menu. As far as I've been able to determine, there's no way to select a script trigger for it directly.
However, as has been discovered accidentally in the referenced discussion, you can select the grouped object button and a field at the same time. You can now assign a script trigger to the grouped object button and the field at the same time. You can then select just the field and remove it.
This leaves you with a button with a script trigger (and my tests show that it is possible to trip at least the keystroke trigger), that cannot be easily inspected to see what trigger was set and what script it performs. (You can inspect/change it by again selecting a field and the grouped object button even though, if the field does not have the trigger selected, you don't see the check box selected, you do see the name of the script.)
While I can't conceive of much utility to having any of these triggers set for a button, this is at best an inconsistent interface design.