Press Home button, phone vibrates -- but only when holding it.

This is a weird one.

I have an iPhone 5S. I pick it up, press the Home button to wake it up, and the phone wakes up (asking for the unlock code) and vibrates. This happens regardless if the Mute switch is enabled or not.

However, if I put the phone on a desk and press the Home button to wake it up, the phone wakes up and DOESN'T vibrate. Again, this happens regardless if the Mute switch is enabled or not.

If I hold the phone in a microfiber cloth or by a suction cup on the back of the phone (i.e., insulating it from my hand as I hold it) then pressing the Home button does NOT make it vibrate.

It's almost as if there's some sort of odd short circuit that's only completed by touching the device. Otherwise the phone appears to work perfectly. Any ideas?