Morning Stu
Welcome to the forum
The BMW parking sensor system fitted to cars of our vintage is flaky to say the least, yours is showing the classic signs of 1 or more sensors being dead. You can turn on the ignition select reverse then put your ear near each sensor you should hear a clicking, no click = sensor not working. If you also have front sensors don't ignore them 1 sensor out means no system.
Which code reader are you using? I use BMW 1.4.0 and I can read and test individual sensors I have a sensor that hates rain, car washes, jet washes and cold weather?? Warm dry weather all OK when I read the codes for the PDC unit it shows "rear centre left" I have changed the sensor no difference so I believe my fault is in the loom some where which with the current weather can wait as I have a reverse camera. Also I have a factory tow bar fitted when I plug in the horse trailer it turns off the rear sensors and the fronts work fine.
When buying your sensors make sure you get the right ones check the part number on www.realoem.com put the last 7 digits of your Vin in the search box and it will bring up your model.
Here is information on mine for what it is worth
Part Number 66206989069 Supersedes:
66216938739
(04/01/2004 — 11/23/2005), Exchangeable retrospectively
66216911838
(09/01/2001 — 03/05/2004), nonexchangeable retrospectively
66216902182
(11/01/1998 — ), Exchangeable retrospectively
66218375533
(03/01/1998 — 01/28/1999), nonexchangeable retrospectively
66218352137
(04/01/1994 — )
Part 66206989069 was found on the following vehicles:
5' E39 (04/1995 — 07/2003)
5' E60 (12/2001 — 06/2007)
5' E60 LCI (04/2006 — 12/2009)
5' E61 (10/2002 — 02/2007)
5' E61 LCI (04/2006 — 05/2010)
X3 E83 (01/2003 — 07/2006)
X3 E83 LCI (03/2006 — 08/2010)
X5 E53 (10/1998 — 09/2006)
Hope this helps
Dave