Do they have any type of special occasion episodes for that matter?

I don't have the episode names handy, but there are 2 episodes MeTV uses for Halloween. In season 2 there is an episode about an older lady who Beaver thinks is a witch. A season 5 episode has Ward and June out for the evening, and Wally with plans to go to a masquerade after a basketball game--Beaver is home with Gilbert, who is going to stay overnight. When Lumpy comes by (to pick up Wally) with a mask on in his repainted car, with Bill Scott, Beaver and Gilbert think they're gangsters, are scared, and call the cops.

As far as other occasions, there is only one--Beaver is in a Christmas program at the end of a season 1 episode, which didn't air in the Christmas season.

The titles for the Halloween-ish episodes are "The Haunted House" and "Beaver's Long Night." And yes, LITB scrupulously avoided holidays and special-occasion episodes.

The closest we see Beaver trick or treating is when Jerry Mathers shows up as a trick or treater on the Ozzie & Harriet episode The Halloween Party.

Some real head scratchers?

No specific holiday-themed episodes?
Not wanting any big laughs?
Childlike gullible Beaver even into his teens. Up to the end of the show's run?

Some real head scratchers?

No specific holiday-themed episodes?
Not wanting any big laughs?
Childlike gullible Beaver even into his teens. Up to the end of the show's run?

True; and a town, Mayfield USA, the state location of which is still debated 64 years later.