Vertical mouse movement makes certain glides much easier to perform but there is no current in-game hotkey to toggle it. It's possible to use scripts or mouse software to avoid this issue.

Is the use of these third party tools allowed?

If not, is one allowed to enable it via the "customize control" menu in the middle of a run and than disable it? (This would take seconds but certain glides save minutes in a run).

You can go into the menu to toggle vertical mouse movement in full game runs. In ILs, however, you would need to have it toggled on beforehand and keep it on throughout the entire run since entering the menu during an IL for any reason will invalidate your run.

As far as I know, no macros or third-party tools/scripts that affect gameplay are permitted.

Thomas is correct. For full game you are allowed to pause and rebind your controls. For IL's it MUST be done before the IL starts. No 3rd party programs or scripts of any kind are allowed to be used during any form of runs.