These are the two replacement regulators available. They usually cover from 01-04 and from 05-09 (07 for V70). Your 05 may fall just in the middle of this, but I would guess it needs the 05-09 one
https://www.fcpeuro.com/products/vol...697015#fitment
https://www.fcpeuro.com/products/vol...637851#fitment
My bet is the right regulator is the one that gives you 13.6v and no light, but something may be wrong with the battery, it may no longer accept a charge - reason why the regulator puts out only the voltage for the car's systems and doesn't try to charge the battery. How do you measure the battery? I disconnect the - cable and measure at the posts