Concrete base for 21' 6x6 wood poles with cross arms
That's more of an engineer's decision to determine wind loads on fixtures, but here's some advice:

Modern commonly available 6x6's are a bad bad bad idea. BAD.  Every knot is a weak point, and will fail in the wind. Not MIGHT fail, they WILL fail.  You need wooden light poles. They are usually locally available for the power companies, and they are just as available to you guys. Price is comparable to a 6x6, they are properly graded lumber, and properly tapered.

Keep in mind that making the wrong decision here could result in injury, or death. Make the wise decision.

Past that, tapering your footing isn't a bad idea, but it can be done simply. Install the Sonatube above ground only, let the concrete go wide to the undisturbed soil below grade.

Size of the Sonatube should allow at least 2" of concrete around the pole, so long as you go the depth you stated.