Just curious where Mr. Pelt’s gourd theist paradigm lies on the cosmological continuum.
I believe that would be a pagan belief rather than animistic. Linus shows no signs of believing that all fruiting bodies have their respective minor deities.
If those are the only two choices, it would be pagan, and a fairly theistic brand of it. Not only was it dubious that the matter of it being pumpkins per se being the critical matter, the physical nature of the pumpkin patch in general didn’t matter. What mattered in the Great Pumpkin’s manifestation was the sincerity of said pumpkin patch. Witness his despair when, flustered by Sally storming off, he suddenly realizes he’s just said if the Great Pumpkin appears; it brings to mind decidedly un-pagan quotes about how a lack of faith is a damning thing.
But keep in mind that older Peanuts strips show Linus as pretty well versed in theology (much of the gang was, in fact; at one point Charlie Brown despaired that he no longer had a baseball team, but instead had a theological seminary, sparked off by Linus quoting from Job). It’s not clear that he viewed the Great Pumpkin as itself a god–I can easily see him considering the GP as a specialized form of angel. Certain denominations of Christianity would probably look askance on that, but others would be right at home with it.
Isn’t animism a subset of paganism?
It’s neither paganism nor animism.
The Great Pumpkin obviously started off as a satire on the commercialization of Halloween and the secularization of Christmas. Thus it has religious overtones, but is not itself a deity or a religious observance.
Belief in Santa Claus is not the same as a belief in a deity, no matter how tied to Christmas he is (or isn’t these days) or how much the trappings or observances of Christianity is brought into the story.
Trick or treating does not imply a belief in wicca or in any pagan celebrations or in early Christian beliefs (as they recasted Samhain as All Hollow’s Eve and all).
As a commentary one step removed even from these limited religious associations and connections, The Great Pumpkin is even less of a religious figure.
The only counterargument I can see is that matters of faith are implicitly (sometimes explicitly) discussed in the cartoons. Can faith be abstracted from religion in general and a specific religion in practice? I would argue yes, especially in a satire in which the target of faith is necessarily an imaginary substitute for the real thing.
I wonder what The Gospel According to Peanuts has to say on this matter?
Can someone summarize what the belief entailed?
Silly!
It’s Pumpkinism! 
AFAIK, he’d sit out in the pumpkin patch on Halloween and wait for the Great Pumpkin to show up and hand out presents. It’s a parody of the whole Santa Claus thing.