Solarized: Night & Day

vimrc

" Set colorscheme to solarized
colorscheme solarized

" Change the Solarized background to dark or light depending upon the time of 
" day (5 refers to 5AM and 17 to 5PM). Change the background only if it is not 
" already set to the value we want.
function! SetSolarizedBackground()
    if strftime("%H") >= 5 && strftime("%H") < 17 
        if &background != 'light'
            set background=light
        endif
    else
        if &background != 'dark'
            set background=dark
        endif
    endif
endfunction

" Set background on launch
call SetSolarizedBackground()

" Every time you save a file, call the function to check the time and change 
" the background (if necessary).
if has("autocmd")
    autocmd bufwritepost * call SetSolarizedBackground()
endif

Instead of repeating the logic that is already in the function, replace your second section (starting "Launch vim with light background...") to just call SetSolarizedBackground().

Always be DRY (Don't Repeat Yourself).

@aaronbieber Ah, didn't think about that. Fixed. Thanks!