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Thin electrode flux penetration effects in Josephson tunneling gates are analyzed and experimental results exhibiting these effects are reported for the first time. Deep flux penetration accompanied by deep current penetration contribute added inductance not coupled to the external field, reducing sensitivity to control current. In addition, the field within the lower electrode reduces the end-to-end asymmetry introduced by the superconducting ground plane and makes the threshold characteristic more symmetrical. The thin film effects are embodied in an equivalent circuit. Experimental results for devices with thick and thin films are compared showing the expected increased symmetry and reduced sensitivity for the thin film case. Experimental results agree well with calculations based on the equivalent circuit.