How can I obtain and set the parting gap of the component through the API or dynamo
can you explain it a bit more. share some screenshots… 
Assume you can get that element, that is a builtinparameter:
Divisions have a builtincategory, so an element collector could get them, but they might not have much in the way of class/API beyond that based on my searching:
I tried to use RIR to implement this feature, but it prompted me that “Parameter ‘Gap’ is not defined on ‘Element’”. I found the API named PARTMAKER_PARAM_DIVISION_GAP, but I’m not sure if it can be implemented using C#.
It looks like the element is divisions as oppose to the geometric element. Try collecting all elements of that category instead and inspect its parameters to see if there’s a way to get it back to its relater elements.