Ok, everyone. Stop speculating please.
For the 1581 the drive must be DS0, also for most Amiga external drives the drive must be DS0.
Redrumloa, modify your drive according to:
http://jope.fi/drives/ju257a606p/There are two smd short circuit blocks that need to be moved and I've put red squares around them. My picture is how it should look after your soldering work.
No cable swap needed, use a straight 34pin cable.
Tested to work with Amigas and the 1581. Don't be alarmed, the drive LED will stay on always with the 1581, just pay attention to your floppy cable orientation. It is marked on both ends.
The drive should burp the stepper motor when you switch it on, if not, your cable is probably the wrong way around or still set at DS1.