I agree with DerStrom - something that is rigidly timer-based fits only a narrow range of driving conditions. This circuit is more of a gentle periodic reminder than a timeout alarm. I haven't given up on the counter-based idea, but a gated 555 is pretty simple, especially when the available input signals are so limited.
D1-D2-Q1 form a NOR gate that enables the 555 oscillator whenever either turn signal connection is grounded. R1 secures the Q1 gate when both inputs are open. D3 makes the 555 wildly asymmetrical - 0.5 s on, 10 s off. While the two timing resistors do interact, it's not by much; adjust R3 for ON time, R4 for OFF time.
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