It was recently demonstrated [Phys. Rev. Lett. 91, 143908 (2003)] that the scattered electric field from highly conducting targets following a rapidly terminated electromagnetic pulse displays a universal t(-1/2) power law divergence at early time. It is now shown that for strongly permeable targets, micro(c)/micro(b)>>1, where micro(b) is the background magnetic permeability, the early-time regime separates into two distinct power law regimes, with the early-early time t(-1/2) behavior crossing over to t(-3/2) at late-early time, reflecting a spectrum of magnetic surface modes. The latter is confirmed by data from ferrous targets where micro(c)/micro(b)=O(10(2)), and for which the early-early-time regime is invisibly narrow.