You haven't provided specific data, but maybe these patterns will suit you.
They are for the version without a rain sensor but this part may match the version with a sensor.
The green BSM plug (3) controls the washer and horn.
At the beginning, in your place, I would check if the ignition appears on the F13 fuse in the BSM voltage - that is, a 21W light bulb and connect it between the F13 fuse and the mass of the car - should light.
As you can see from the diagram from this fuse goes power to the R4 relay built into the BSM which controls the sound signals. Then the power rushes to the BSM socket on pins 7 and 15.
Then check the same fuse F14 in BSM, which supplies the built-in relays in BSM - R9 and R10 controlling the washer pump. These relays are used to change the voltage polarization at the BSM output where the pump is connected to change the direction of rotation - as you can see at the BSM output in normal state on both pins we have mass and now depending on which sprayer you turn on, the R9 or R10 relay is activated.
You wrote that the sound signal relay is ticking so it is possible that the power supply from the fuse does not reach it, it has a burned working contact or the wire between the wild signals and the BSM is broken as long as they have ground.
Attachments:
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Spryskiwacze 307.pdf
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BSM 307.pdf
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Klakson nikotonowy 307.pdf
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Klakson wysokotonowy 307.pdf
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