How do I insert a tab character in Iterm?

The answer was to hit control+v, then tab afterwards, not all together! Hope this helps someone.

It's not iTerm, but your shell that affects how you''re able to insert a tab.

First, make sure you're in BASH shell: Type the following command:

$ echo $RANDOM $BASH_VERSINFO23714 3

The first is a random number, and the second should be the BASH Version number. If you get a blank line or just a random number, you're not in the BASH shell, and that's probably one of your issues.

Another thing is to execute this command:

$ set -oallexport       offbraceexpand     onemacs           onerrexit         offerrtrace        off[...]privileged      offverbose         offvi              offtrace           off

The two lines of interest is the emacs and the vi lines. One of those should be on. If they're both off, you can't do the Ctrl-V-Tab to insert a tab character.

When the vi mode is on, it should be Ctrl-V-Tab like you said. With emacs mode on, it is either Ctrl-V-tab, or possibly Ctrl-Q-tab.

However, this isn't an iTerm thing, this is your shell that's doing it.

If by a "physically real tab character" you mean sending the tab hex code (0x09) to the shell, then you can do this in iTerm by pressing Ctrl + Tab (⌃ ⇥).

This is the default setting, although you can change it (as well as add other hex code values to send) in iTerm > Preferences > Profiles > Keys.