Start pulling fuses until you find the circuit that is the culprit. Then take a look at each item in that circuit... In this case, it sounds like you've done that and/or the circuit is not fused! In this case, it sounds like an alternator diode may be bad, or there is a relay coil which is either latched or in circuit to hold the contact closed. If not, then I'd check by pulling the coil wire, or your ignition. How are you measuring the 2 amps? Do you have an ammeter in the dash?