Binding f2 u

[Steve Wainstead <wainstead@gmail.com>]

I'm trying to bind "f2 u" to a custom function. After spelunking the
*Help* and googling, it seems F2 is the prefix key for the sparse
keymap "2C-command," or else "2c-mode-map."

By default, when one starts emacs -q -nw, f2-s starts two column mode;
so something must live in the global map? Because I cannot bind
anything to either 2C-command or 2c-mode-map:

(define-key 2C-command "u" 'sw-update-builds)
or
(define-key 2c-mode-map "u" 'sw-update-builds)

These fail because 2C-command  and 2c-mode-map are void, while:

(define-key ctl-x-map "9" 'sw-update-builds)

does work. How can I bind to f2-u without wiping out the existing mode
map, which seems to be undefined even after I load 2 column mode? I'll
wind up just creating my own sparse keymap for f2 otherwise.