We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study susceptibility scaling in a trapped two-component Bose-Einstein condensate. This system supports a second-order phase transition between miscible (cospatial) and immiscible (symmetry-broken) states that is driven by a diverging susceptibility to magnetic fluctuations. As the transition is approached from the miscible side the magnetic susceptibility is found to depend strongly on the geometry and orientation of the observation cell. However, a scaling exponent consistent with that for the homogenous gas (gamma = 1) can be recovered, for all cells considered, as long as the fit excludes the region in the immediate vicinity of the critical point. As the transition is approached from the immiscible side, the magnetic fluctuations exhibit a nontrivial scaling exponent gamma similar or equal to 1.30. Interestingly, on both sides of the transition, we find it best to extract the exponents using an observation cell that encompasses half of the trapped system. This implies that relatively low-resolution in situ imaging will be sufficient for the investigation of these exponents. We also investigate the gap energy and find exponents nu z = 0.505 on the miscible side and, unexpectedly, nu z = 0.60(3) for the immiscible phase.