Just like the title says:

How do you tell how many visitors used the search function on our website? Or how many times the search was used for any given month?

I have google analytics installed and cpanel access and have scoured all the reports with no luck. I thought I found it when I used site overlay, but for some reason it doesn't show how many times people clicked the search button.

Thanks in advance for any insight!

Well it doesn't tell you number of searches, but it does tell you what terms were used in the stats in the cubecart admin panel.

Do you have any kind of page counter on your site. i am using statcounter and its free.