How can I highlight the current cursor position (not just the line)?

Question

When I search a text file for a word from within Vim, it will highlight all matches for the word by changing their background color -- to olive green on my terminal; your color may vary. I am looking for a way to highlight the background color behind the current cursor position in this way. (This would make the cursor easier for me to see than it is by default.)

By reading the Vim documentation and searching the web, I found plenty of information on highlighting the line the cursor is currently on. But that is not what I'm looking for right now. I am specifically looking for a way to highlight the character at the current cursor position, specifically by changing its background color in the way Vim already does with matches to text searches

How can I do that?

Answer 1

You can turn on search match highlights like this.

:set hlsearch

To turn it off until the next time you search, use this.

:noh

To change highlight to a specific color:

:hi Cursor guibg=#rrggbb
or
:hi Search guibg=<colorname>

Answer 2

Here's a quotation from the vim's built-in help that will probably answer your question, if I actually got it right:

When Vim enters Insert mode the 't_SI' escape sequence is sent.
When Vim enters Replace mode the 't_SR' escape sequence is sent
if it is set, otherwise 't_SI' is sent.  When leaving Insert
mode or Replace mode 't_EI' is used. This can be used to change
the shape or color of the cursor in Insert or Replace mode. 
These are not standard termcap/terminfo entries, you need to
set them yourself.

Example for an xterm, this changes the color of the cursor:  

    if &term =~ "xterm"
        let &t_SI = "\<Esc>]12;purple\x7"
        let &t_SR = "\<Esc>]12;red\x7"
        let &t_EI = "\<Esc>]12;blue\x7"
    endif

NOTE: When Vim exits the shape for Normal mode will remain. 
The shape from before Vim started will not be restored.

{not available when compiled without the |+cursorshape| feature}

I already tested this and the only issue I see is that the original color of the cursor isn't restored upon exiting vim, as already noted above.