Step 1: Erythema annulare centrifugum is an asymptomatic or mildly itchy eruption of variable duration. It begins as red papules that spread peripherally while clearing centrally, producing annular, arcuate or polycyclic plaques that enlarge slowly at about 2 to 5 mm per day. The chronic, asymptomatic, centrifugally spreading lesion described here fits it best.
Step 2: Erythema migrans is usually less numerous, less circinate and is linked to a tick bite (Lyme disease), so the long standing buttock lesion without a tick history does not fit. Erythema gyratum repens spreads much faster, has a bizarre wood grain pattern and is almost always tied to an underlying malignancy.
Step 3: Erythema marginatum is a non scaling gyrate erythema seen specifically with rheumatic fever, which would present acutely with carditis or arthritis rather than a slow chronic plaque. By exclusion and by the classic centrifugal spread with central clearing, the diagnosis is erythema annulare centrifugum.