Now, if I:

- byte-compile this file,
- M-: (package-generate-autoloads "testautoload" default-directory)
- emacs -Q -L .
- M-: (load-file "testautoload-autoloads.el")

then:

- global-testautoload-mode is t,
- the testautoload-mode variable is undefined,
- the testautoload-mode-map keymap is undefined.

From there, (customize-set-variable 'global-testautoload-mode t) enables
the mode in all buffers and the keymap works.  Is there a way to do away
with this extra step?  I've messed with :require and :initialize, but
they don't help AFAICT.

What does help is adding this snippet at the bottom of my library: