The pin head(the wide part) should be approximately .235" diameter, so a little less than a 1/4". The length should be 3/4". If the pin head is larger diameter, it's not the right one. Replacement pins of the correct diameter sometimes still have to be shortened to the 3/4", since they make them longer so they'll fit more applications and you cut to size.
The pin head should fit inside the tube and move freely if it's the correct size. You must lock it into the notch in the tube with that little black plastic lock. The pin needs to spring up and down, so it can't be stuck tight. If your pin is the correct size and still doesn't fit, your cancelling cam tube is probably damaged, so you'd need to replace the cancelling cam, which the tube is part of.
This is how it works. When you install the wheel hub, the tube and pin sticks up through the hole in the bottom of the hub of course. (Be sure that the little alignment mark in the center of the hub lines up with the alignment mark on the top of the steering shaft when you install the hub). Because of the protruding tab on the tripod, when you install the tripod, the tab must fit into the channel in the side of the hub, so the tripod only fits one way. That's important since it must only be installed in that orientation. The tripod sits over the spring loaded pin, so the pin is always touching the bottom of the tripod. When you install the steering shaft nut in the center of the tripod, the tripod is grounded to the steering shaft and the hub. The tripod is spring loaded too. The part of the tripod that the pin contacts on the bottom is isolated from the ground. But when you push down on the tripod, the discs inside the tripod make the ground connection which transmits a ground signal to your contact pin which is distributed from there out to the horn relay, and your horns blow.