The relevant code section is 210.70 A, 2, c
(c) Where one or more lighting outlet(s) are installed
for interior stairways, there shall be a wall switch at each
floor level, and landing level that includes an entryway, to
control the lighting outlet(s) where the stairway between
floor levels has six risers or more.
Exception to (A)(2)(a), (A)(2)(b), and (A)(2)(c): In hallways,
in stairways, and at outdoor entrances, remote, central,
or automatic control of lighting shall be permitted.
So there is no dimension listed, only the entryway is listed.
As a practical matter, all stairways are required to have a handrail.
Whatever supports the handrail could be used to support the switch as well.
Most inspectors would frown on the switch being 12' away, as well as it being a pain in the **** for the user. Install a post for the handrail support and mount the switch on it, problem solved.
MTW Ω