He shows up when you first enter the island, getting his party invitation. But you will not see him again until you finish the process with Linus and the Pumpkin Patch.
You have to choose a pumpkin for Lucy and roll it safely to her house. Then take Linus's bag and give it to Pigpen, and the lemon sucker back to Linus. Once you have his invitation, and the pen, you can go left into Charlie Brown's back yard where he and Snoopy are gathering leaves.
The name of the island is Great Pumpkin Island. See the related question below.
'It's the Great Pumpkin, Charlie Brown' debuted in 1966.
Charlie Brown awaits the arrival of 'The Great Pumpkin' .
Snoopy
The Great Pumpkin?! that's from charlie brown.
No.
Charlie Brown is on the sidewalk when you enter Great Pumpkin Island, but he spends much of the game in his back yard left of Main Street. Snoopy is at his dog house at the far left of the island. Your first task is in the pumpkin patch to the far right. You have to weigh the pumpkins, roll one back to Lucy's house, give Pigpen the bag, and give Linus the lemon sucker. Then you can go left where Charlie Brown is collecting the leaves with Snoopy.
linus
Rocks
To get to Charlie Brown's backyard, go left past the Flying Ace cafe. You need to complete the pumpkin patch first, then get the pen and invitation, before you can do the Snoopy and Charlie Brown scenes. (see related question)
After Linus mails his letter, go left to where Lucy and Charlie Brown have the football.
You are drawing on his head -- the pumpkin gets carved the same way. Whatever face you draw will work.