Hmm, yes, that might sound good!
But why is "him neither" wrong? I was told I can use "neither" with pronouns, but I'm not sure about other subjects:
She doesn't have a car. And him neither. = He doesn't have a car either.
<-- Should be ok.She doesn't have a car. And John neither.
<--- Not sure it's ok, I guess it's not.
![Smile [:)]](/emoticons/emotion-1.gif)