I take it this is a phenomenon that is actually happening and not a performance request?
Resonant peak? You would likely have the same affect on all guitar positions for "that note" and not just the twelfth fret. This is hard to accommodate without schematic analysis though
Acoustic feedback? It's always possible that the guitar and amp have a symbiotic resonance. If this were the case it would only present itself with the one guitar. Possibly only in that one room.
The amp has no idea what position you're playing in. Wolfing notes and ringing notes are almost always related to the guitar itself. Only the guitar knows what position you're playing in and there are all sorts of resonant peaks that differ from instrument to instrument. From a physical, rather than electrical standpoint it is much more possible to have note anomalies sensitive to position. It may not be evident with other amps because they have a different frequency accent than the amp in question. It's possible (probable) that the guitar has acoustically resonant characteristics that are especially evident with that particular amp.