The first accurate measurements of the α-decay branching ratio and half-life of the I^π=1/2⁺ ground state in ¹⁸¹Tl have been made, along with the first determination of the magnetic moments and I=1/2 spin assignments of the ground states in ^177,179Au. The results are discussed within the complementary systematics of the reduced α-decay widths and nuclear g factors of low-lying, I^π=1/2⁺ states in the neutron-deficient lead region. The findings shed light on the unexpected hindrance of the 1/2⁺→1/2⁺, ¹⁸¹Tl→g¹⁷⁷Au^g α decay, which is explained by a mixing of π3s_1/2 and π2d_3/2 configurations in ¹⁷⁷Au^g, whilst ¹⁸¹Tl^g remains a near-pure π3s_1/2. This conclusion is inferred from the g factor of ¹⁷⁷Au^g which has an intermediate value between those of π3s_1/2 and π2d_3/2 states. A similar mixed configuration is proposed for the I^π=1/2⁺ ground state of ¹⁷⁹Au. This mixing may provide evidence for triaxial shapes in the ground states in these nuclei.