The trigger for the Tiger's main gun was adjacent to the elevation handwheel. The gunner could fire without releasing his grip on that wheel.
This is the gunner's position, looking down, in an early Tiger. Two foot pedals are at the lower left of the photo; the side of the gun assembly is at the right; and under it we see the elevation wheel. The gunner operates it with his right hand.
Looking more closely at the wheel, we can see that there's a mechanism behind it.
From the other side, we can see an arc beside the wheel (arrowed). That is the trigger bar.
This diagram is taken from the Tiger Turret Manual and it shows the trigger bar. You can see that it's hinged, and is held away from the wheel (which is not drawn) by a spring. When squeezed together with the wheel, the bar will press a button on the trigger lamp at the bottom of the mount.
In mid 1943 the Tiger's turret was redesigned, with many changes including a new cupola. The trigger mechanism had been mounted on the end of a thick metal pipe. The pipe was now eliminated. Instead, a welded bracket was attached to a nearby crossbar. It carried the trigger, the handwheel and the lamp box in exactly the same spatial locations as before.
This photo was taken from directly ahead of the handwheel, and is valid for "Mid" and "Late" Tigers.