Does the resistance vary as you move things around or just over time with the leads held steady? I can't imagine a scenario (with a GOOD coil) in which the resistance should vary much at all either over time or by moving the wire around...
If the coil has a finite capacitance, then you should see the resistance change a bit over time as that capacitance charges up, but the measurement should settle out to a stable value after a short time.
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