Search has, over the years, been over-designed. One common anti-pattern is hiding search behind a control to activate it. Slowing the user down and adding an extra step might remove an input field from your view but at the expense of familiarity.

If you're offering your users a search function, then show them a text field with a search button. If you're using an icon, then use a "magnifying glass" icon. This is the archetype and using anything else makes no sense anymore.

On a mobile phone screen, there may not be enough space to always show the search field, but I'd still encourage you to evaluate if you can. Tucking the search field into the top of a scrolling view can work well:

Bonus points: when the user taps the Search tab in a mobile app, show the search view, move the cursor to the search field and show the device keyboard for them.