Parking to load or unload equipment at the Tate loading dock requires a loading permit, which is good for 30 minutes. The department has one - if you need it, sign it out from Ginny.
PAN has “Vendor parking” for which the loading dock pass is not valid. Also note this is really close to the Facilities Management nerve center beneath Mech Eng, and it's very likely an official university vehicle will show up and want to use them. Trying to use these spots without an appropriate pass is likely to be ricky.
Please remember that blocking the loading dock at either building with a passenger car, with or without a loading dock pass, is a really bad idea. If you are using a pass, try to park your car to the side, to leave the dock accessible for trucks. At PAN, this would be in front of the smaller door intended for dumpster access.