How do I make an extract to get the flavor of a pumpkin? Should I use pumpkin seeds or fresh pumpkin or maybe even the pumpkin skin? If I use pumpkin, should I dry it out or dehydrate it?
This is speculation, since I have never done it, and I don't think it is practical or more effective than just cooking with pumpkin puree for these applications.
If I were to try this, I would:
I suspect the results of this would be underwhelming. You will note that this is essentially how fruit liquors are made at home, except for step 1 (unique to pumpkin) and step 4.
For curiosity, see also this recipe for a pumpkin liqueur, although it also has many additional pumpkin flavors. The key difference is you won't use extra flavors, and you will use a much higher pumpkin to solvent ratio.
The pumpkin flavor you're likely looking for is nothing more than the spices that are added to pumpkin "stuff": cinnamon, nutmeg, cloves, etc. If you attempt to do an extract to achieve "pumpkin essence", you will not be happy with the results.
I have been a home brewer (beer, wine, mead, etc.) for 20+ years and have seen many attempts from various brewers to make a "pumpkin beer". Long story short (and you can do a search and verify what I'm saying on any beer brewing forum's out there), it's the spices that make the flavor, not the pumpkin squash fruit.
Bottom line is there is no "typical anticipated pumpkin flavor" imparted by just pumpkin. To make a great pumpkin beer, the guys who have made multiple batches of pumpkin beer using varied recipes (using chunked up pumpkin, cooked pumpkin, roasted pumpkin, etc.), all ended up finding the perfect pumpkin beer was made using only the spices and not even using any pumpkin at all.