Hirsty, I asked a lawyer about this.
His advice was definitely pay the IBI bill, as that will bolster your claim, as you rightly point out.
You can claim it as yours after 10 years providing the owner lives in Spain. If the owners lives abroad (overseas) it is 20 years.
Through a law court procedure, neighbours’ witnesses will be required that you have been using it as your own. That ruling is then lodged at the Land Registry and the change of ownership takes place.
More on this subject: Adverse Possession Explained by Raymundo Larraín Nesbitt