I think you have a display with 2 lines of 16 characters.
On the backside of the display you can find only one drop of black plastic.

The Controller (under the plastic) can NOT manage these display in the desired way. The display ist broken into 4 parts of 8 characters.

look at this:
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;Display clear
Disp_Clr:
LCDOUT $FE,1isp_Zeile2=0:Return
;goto the second (right) part of a line
Disp_Tab:
LCDOUT $FE
IF Disp_Zeile2 THEN
LCDOUT $C8
ELSE
LCDOUT $88
ENDIF
return
;goto the second line
Disp_LF:
LCDOUT $FE,$C0isp_Zeile2=1
Return
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