Does the train Engineer have a switch in the locomotive to turn off the crossing lights?

There's no switch inside the cab to turn crossing lights on and off.

What you likely saw was something called a "timing circuit". Most crossings are timed so the warnings are active for at least 20 seconds before the train occupies it. Some crossings where the trains are likely to stop short of it, have these timing circuits, so if the train does not pass a second point on the rail leading to the crossing by a certain point, the crossing "times out", the lights go out, and the gates are raised.

There are also crossings which can be turned off by way of radio, but there's not that many around. The engineer puts his radio to a certain channel, then dials a certain tone (radios have number pads like a phone, you can "dial" various numbers like you would on a phone), along with a number unique to that crossing, and something in the signal hut responds to the tone.

Budgie is spot on with 10 points on the way.

One thing to add, however. In those instances where the gates have "timed out", some crossing protection is equipped with a microphone that will restart the protection by the engineer blowing the whistle.

There is a safety issue here as well. If there are multiple tracks involved, the standing train is seriously reducing your field of vision at the crossing. Requirement of equipment standing at least 150 feet from the crossing is not always possible, creating a dangerous situation. The problem is when motorists see the crossing protection, see the train that is stopped, and go around the gates. The result is an automobile turned into graphite and one or more people joining the ranks of the dead for that statistic keeping period as they discover a train on the other track. Splut!

Some systems detect a train by sending a signal down one rail, and the signal goes through the wheel and axle to the other rail where it is received back at the crossing. Using the doppler effect, it can tell how fast the train is going and how soon it will arrive. If it stops, the signal is received back at the same frequency and the system nows the train stopped. Once the train starts, the systems knows it is again moving, and will drop the gates. Unless it's backing up.

As mentioned previously a couple of times, Budgie is on point. There aren't any switches on the engine that control crossings. Chances are the crew on the train were waiting to be relieved or possibly waiting for another train to pass them. When a train goes into a siding we call it "going into the hole". A couple of people mentioned sound activated crossings and radio controlled crossings, I'm a conductor for CSX in central Florida but, all of the crossings I've seen are circuit controlled. We don't have any radio controlled crossings either that are in our timetable but we do have a couple yards that use radio controlled switches.

No it doesn't, the rails have a continuous current running through them which is conducted through the wheels, so if the train is moving at a certain speed the gates go down when the train trips the sensor on the rail, and adjust to the speed of the train.

Conductor Budgie is the only one to get it right so far.

NO, there is no switch in the locomotive.

As he said, there is a timing circuit in the crossing relay hut, or a few with a radio de-activation.

No way are the signals controlled from a train! The engineer of the train you saw must have tooted his hooter a few times and some signal cabin must have given him the go ahead by changing the signal.

Yes it has an switch

No !!