E30 fuel gauge

My 320i, 1987 model has recently started to show very varying fuel readings when it nears the empty mark. It is almost as if the gauge swings left and
right as the fuel splashes from one side of the tank to the other. Is there an easy solution to this problem?
If the tank is above half full, the fuel gauge does not behave like this.
Kind regards MW
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I'd remove the level sensor and clean it. If you remove the rear seat bottom you'll find an access panel.
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