So after some further investigation, It seems that it is indeed a secondary pump attached to the washer fluid bottle, I'll need to drill the correct size hole for the new pump (pressure fit via rubber neck), or just get one along with the other parts and swap the whole thing.
There is still the issue of the connector for the second pump not being present on the JDM spec vehicles or any FRS version for that matter.
So I'm thinking to get the correct connector and instead run a new line from the secondary pump to an interior button, connected to a 12V source so that the headlight washer can be activated independently of anything else as long as the car is running.
The question of whether the bumpers have markings for cutting a clean, correct hole for the actuators has an answer too!
Turns out they do!