I have this note from years ago sent to me by 200mph reminding me there are two different L3240's.
When referencing the Grand L40's there are two different submodels for this series and not all information is consistent between them. They came in L3240-1 and L3240-3 (in US at least). In some situations, it might make sense to verify the submodel just to make certain the correct manual is referenced. How PTO engagement is activated is one way of confirming the difference (besides SN). -1 uses a manual lever and -3 uses a rotary electrical switch
Before anyone checking for a wiring diagram, best to post what model you have.
Your symptoms sure sound like a bad battery connection.
Do you have any cable ends like this one?
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These historically have been bad news over time,
Dave