I would look into the jQM Documentation for Events, the current docs are here:
for a Mobile device use touch events, if you need mouse events jQM provides Virtual mouse events for this as well.
Virtual mouse events
We provide a set of "virtual" mouse events that attempt to abstract away mouse and touch events. This
allows the developer to register listeners for the basic mouse events,
such as mousedown, mousemove, mouseup, and click, and the plugin will
take care of registering the correct listeners behind the scenes to
invoke the listener at the fastest possible time for that device. In
touch environments, the plugin retains the order of event firing that
is seen in traditional mouse environments, so for example, vmouseup is
always dispatched before vmousedown, and vmousedown before vclick,
etc. The virtual mouse events also normalize how coordinate
information is extracted from the event, so in touch based
environments, coordinates are available from the pageX, pageY,
screenX, screenY, clientX, and clientY properties, directly on the
event object.
I'm not saying the 'click' event wont work as it still does, for example you can click a button. But there will be different events for Mobile devices verses Desktops