I have several A590 units and unless you set the DIP switches correctly the sidecar won't boot.
Only DIP switch number 1 should be in the up position and on.
Switch 01: Is for selecting the boot WB required after WB1.3
Switch 02: Selects external drive unit numbers so if nothing plugged into the SCSI it should be off.
Switch 03: Is a delay for drives that require such a thing. So switch can be off.
Switch 04: Is reserved for future use and should be off.
https://www.scuzzscink.com/amiga/scuzzblog_november24_1/car_sbd_061124_04.jpgNow I have several of these units and I actually have one that appears to be wired incorrectly. Only when I set switch 1 to OFF and the rest to ON would it work. And that is when I discovered that if the swiches are not correct the unit will not boot.
Not sure you have the manual.
https://www.scuzzscink.com/amiga/car_libs_012.htm