Hi Andie,
You can use same outbound plug for both fields but problem is system will always set the same field irrespective of which F4 help popup you clicked in web ui. Reason behind this you are calling the same close event code and there only you have added code to set partner number and partner function if i am not wrong.
So i would you say you can use same outbound plug but you need to differentiate both fields F4 help search events so that you can set the partner function value based on the field clicked in web ui. Otherwise you can copy the existing outbound plug which is working and give different close event name and try. If you are facing still any issue let us know.we can give some inputs.
Best Regards,
Dharmakasi.