The best method would be to download a marker/calligraphy brush set like this one.
Then you could use it to paint out your pattern.
Alternatively you could create a pattern and then adjust the pattern to fit your needs. This can be accomplished fairly quickly with a few steps.
Note, this is only one of MANY methods to accomplish this.
To start, download the brushes from here and then open them up from your brush panel.
Then create your stroke lines for the pattern using one of the brushes. It might take several tries to get a line you like. Just Ctrl+Z and redo until satisfied.
Then group each of the pairs of lines together using Ctrl+G and move the pairs into a rough square position.
You can also add some rotation to break up the rigidity of the pattern.
Now select all and again Ctrl+G to group the strokes. Navigate to
Window > Pattern Options and go through the dialogue menu and select done.
Now we have a pattern swatch saved for us to use. Open the swatches panel if it is already not open by going to
Window > Swatches. Then create a rectangle using the
Rectangle Tool (M) to your desired size. Click the fill option and select our swatch.
And there you have it, one quick and dirty method to making your effect.
I highly recommend checking out this other post on GDSE:
Random pattern generation in Illustrator
It links to some other articles and resources to further improve on this method.