Is it possible to simulate touch without root? Is there any way to simulate a touch (anywhere) on the screen without root?

If not, is there any other way I can perform a cardboard 'select' action without magnet support, or opening up my cardboard every time?

Background

I am trying to get cardboard apps to work to work with a 5.1 phone which doesn't support the magnet 'button'.

Most apps seem to use the button to select or advance, so without it working, it is difficult to use. I have found that a touch anywhere on the screen also works as a select, so what I'm doing at the moment is opening the back, touching the screen and then closing it up again, but obviously that quickly gets tedious.

What I have tried:


Using my ipega 9017 gamepad (in Gamepad, Keyboard and iCade modes) no mode maps any key to anything which performs a select action in cardboard (though some modes map the B button to back, which works to exit a cardboard app at least).
I have tried Tincore Keymapper, but that requires root in order to simulate touch, and I cannot root my device.
Looking on here, custom keymapping for games?, Can I use USB gamepad without any setup? and Mouse to touch? looked most promising, but none of them answer this question.
You can potentially simulate a touch with the command input tap x y (e.g. from a terminal emulator, or possibly with Tasker (can't remember if it can do shell commands, but I presume so)), or over ADB with adb shell input tap x y. See https://stackoverflow.com/a/20830258/2141741 (and if you want to connect the device to itself via ADB, https://code.google.com/p/android/issues/detail?id=48126 and associated comments are informative).

This solution doesn't require root (at least not doing it from a computer connected over ADB).