Unless your jQuery is at the end of the document, remember to wrap it in jQuery(function($) {...}).
Attach all event handlers in javaScript, not HTML. This is not essential, but allows you to see all your interactive code in a single glance.
Stay aware that .play() and .pause() are <video> element methods, not jQuery methods.
Try this :
HTML
<div class="topVid channel1960s">
<div class="testMarqueeLeft">
<div>CHANNEL 1960s: Jackie Kennedy at JFK's service</div>
</div>
<video loop> <!-- remove onclick="..." -->
<source src="videos/1960s_Jackie_mourning_VERT.mp4" type="video/mp4" />
Your browser does not support the video tag.
</video>
</div>
JavaScript
jQuery(function($) {
// Attach click handler to both <video> elements
$('video').on('click', function() {
this.paused? this.play() : this.pause();
});
// Attach click handler to top video's prev/next buttons
$("#nextButtonTop, #prevButtonTop").on('click', function(e) {
e.preventDefault(); // maybe not required but does no harm.
var $video = $('.topVid video');
if ($video.is(':hidden')) {
$video.get(0).pause(); // .pause() is a method of the <video> element, not a jQuery method.
}
});
});