Your Golden Flash would have been positive earth originally.
Presumably it was converted to negative earth at some point in the past, as many owners are more familiar with neg. earth systems these days.
So just reversing the battery polarity probably won't cure the problem if there is a fault elsewhere, such as a failing rectifier (or does it have a dynamo?) or a partial short somewhere that could also be causing the battery to drain quickly but not blow the fuse (it is fitted with a fuse, isn't it)?
If your Flash has a dynamo, (instead of an alternator & rectifier) then the regulator could be faulty?