1. spawn core
2. add inner ship remote, name it and add it to the hotbar
3. for demonstration purposes, add a cube light and connect it to the remote
4. enter flight mode if not already there
5. select inner ship remote hotbar button, click to confirm it works
6. switch to build mode
7. (left-)click on the ship or the UI; result: inner ship remote registers click, light toggles
8. expected result: inner ship remote ignores clicks

Observations: The clicks don't seem to always register if you click on some UI elements, but usually the second or at most third click on that same element goes through to the remote. Clicks that would place blocks (regardless of whether a block is actually placed, e.g. if you click into empty space, or if the selected slot isn't a placeable block) always register.

2 ship hotbar items that still react to mouse clicks outside ship mode:

1. Inner remote (as reported above)
2. Rail turret axis

The inner remote toggles with your mouse clicks even outside ship mode, assuming you have that slot selected before you go to build mode or menus.
Rail turret axis does not fire with mouse clicks, but turrets still follow your mouse cursor in build mode.