At what option count should I add a search filter to a drop down element?

I have a booking tool that offers a list of services to choose from. The option list is variable per client. Some clients offer one service, some have twenty or more. One client requested a search filter on the drop down. We are honoring the request and it will go out to all users.

However, I don't want to add a the filter unless it's useful.

So, at what option count does the search filter become meaningful? I am setting that number as a constant and if the option count reaches it, the search input appears. I chose a number that is A. less than the clients service count of course :) and B. What I think is the right count but I wonder if my choice is arbitrary.

What is your number and why?