Save Bash shell history also when closing Terminal tab

The approach given here looks a little simpler—maybe it would work for you?

If you don't want to remember to type "quit" instead of "exit", and you're using bash, just add the following to your .bashrc or other shell startup script:

trap '/usr/bin/osascript -e "tell application \"terminal\" to quit"' 0

What's it do? When the shell receives signal 0 (zero), that is, told to exit, it will execute this command as the last thing it does. This allows your shell, etc, to exit gracefully, and asking Terminal.app to exit via applescript makes sure it does the same. In other words, type 'exit', and your shell exits, then Terminal quits, all cleanly and the way nature intended.

The full thread can be found here.

You could add something like this to the startup script of your default shell (mine is zsh, most people use bash, I guess, so you may have to tweak.)

Here's my bit of screen jiggery-pokery (in my .zshrc)

# Autoload screen if we aren't in it.  (Thanks Fjord!)
if [[ $STY = '' ]] then screen -xRR; fi

I got this from somewhere on the interwebs (I don't recall where, and I don't know who Fjord is, but good on him.

With this you can close your iTerm window, and it will resume where you left off when you reopen it. I highly recommend reading the screen man page also.