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connecting the batteries in parallel would work as 12V, but the problem then would be that your charger is 24V and will knacker the batteries unless you replace it with a 12V charger. this may also entail modifications to the charging module in the unit as well.
that thing at the bottom left-- a solanoid?-24 volt windings?
Basically you need to achieve this;
(sorry about the drawing). Which wires you use to make the connections is your choice & depends on length but please ensure that they are the same csa otherwise hey will overheat & posible catch fire in high current applications.
As previously mentioned you will need a 12V charger as a 24V charger would overcharge both batteries & buckle them beyond beliefe!
View attachment 16473
......Andy ;~)