I think the pole is in the game and it is tinkerable.

But at the moment I'm at a loss as to what to try in terms of a formula.

Some thoughts I have about different components are:

Fishing poles - It seems resonable, I suppose, if your looking at the
collapsable fishing pole as a modification of an existing pole. Or perhaps
from the standpoint of cannibalizing the reel and string from a pole.

Shafts - I think so, just from the statement that the pole was comfused
with a spyglass, which operates on a telescoping mechanism.

Rods - Well, the pole is very light and flimsy, thats why you have to add
an extra rod to support the weight of a bottle, lens and twine in order to
make a spyglass. So I don't think a rod is in the recipie

Gears - If a fishing pole is in the recipe because the reel is being
cannibalized I don't see any logical reason to have gears

Sprocket - Same as gear

String - possibly... depends on weather or not the fishing line is
cabbibalized from the other fishing poles in the recipe. At any rate I
doubt it is the metal twine, more likely its a clothe twine or cord or
silken thread of some sort.

Cork - could be a possibility

Spricket - what the hell is a spriket?

Bolts - Its possible that if the reel is cannibalized from an existing
pole, that a bolt will be needed to mount it to a shaft

Grease - Also possible to lubricate the shafts so that they collapse easily.

Raw bamboo - another possibility

Price for pole: I bet it doesn't cost much more than 5 plat to make, and
is an easy item like the lantern and compass.

I think the decision that needs to be made is this:

Is the collapsable fishing pole a modification of a regular pole

or

Is the collapsable fishing pole something created entirely from tinker
components

The reason I think this question needs to be answered is that if it is a
modification, then we need to look at parts that would follow that line of
reasoning.

Rotgut