Silly comments

I'm a Spanish speaker, and this question comes from a prestigious member wearing the "GB" letters in his name, so I'm intimidated. But anyway ...
In Spanish, quite informally almost humorously, I use the verb picar that means to beakto peck. Mouse pointers and fingers behave like birds while eating.
Now I realize that this silly word pictures both actions.

Serious comment

What I wouldn't use is select, which was nominated several times above.
To me select is what happens immediately after you beak on a Windows icon (for example): it changes it appearance in order to look as a selected icon.

My answer

In some IT applications there are property sets that contain, among other data, some word for items.
Like for example the word for scripted actions is "sh" in *NIX, "bat" in PC DOS, "job" in mainframe.
Web apps can be sent a property bag with words for things that are slightly different in the various clients, and do replacements after having recognized the media.
Thus, in UIs equipped with touch screens (not necessarily mobile) the name of the thing would be tap while in mouse-operated UIs click.
Something like i18n, isn't it?

This is not to say that it's possible to do a knee-jerk replacement of every "click" by a "tap". The replaceable instances must be carefully tagged.
Also, if the UI was going to be translated, English is a best scenario where click can be used as a noun and several verbal forms too. It's not so in Spanish where you would need several words.