There is only one feed to the high/low switch (then on to the headlamp) from the relay; the switch simply determines which of the two filaments in the H4 bulb receives current. If the high beam works with the engine running, but not the dip, it is not going to be the relay.
I would suspect either: (a) The dip filament has failed in the bulb; (b) There is a fault in the handlebar switch; (c) There is a loss of continuity in the dip beam wire from the switch to the bulb holder (bad connection or break); (d) There is a fault in the bulb holder (corroded contact/loose connection)
BTW - The headlamp flash (or pass) switch is a bit of a ' red herring' as it has a separate supply and bypasses the relay altogether.
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