And here are a couple of traces showing how the relay coil affects the supply to the 555 timer circuit. I've gone down to 1 volt/div for these traces to show the voltage drop a bit more accurately, and timebase is now 1 second to show the relay being triggered for the intermittent wiper approx. every 5 seconds.
The first trace shows the effect of having the relay on the filtered (555) supply. You can see how the supply voltage to the 555 circuit drops when the relay is activated for half a second or so. I guess as more current is drawn by the load on the RC filter more voltage is dropped across the series resistor of the RC filter, and the less voltage the 555 circuit gets as its supply. Note that this placement of the relay causes the 555 timer to pulse the relay every 4.6 seconds (quicker than I wanted):
...And for comparison, here's the same circuit out of the car and connected to a clean bench power supply (timing pulse increases to 4.8 seconds with cleaner supply):
The trace below is when the relay has been moved off of the clean 555 supply and on to the noisy car supply. The supply to the 555 is affected a lot less, and subsequently the timing of the 555 circuit is much more accurate (around 5.4 seconds):
...and for comparison, here's the same circuit out of the car and connected to a clean bench power supply (timing pulse increases to 5.5 seconds with cleaner supply):
So in summary: Success! An RC filter to clean the supply to the 555 timer circuit and the addition of a PNP transistor to switch the relay coil on, with the relay coil now connected to the noisy supply so that it doesn't affect the supply to the 555. I've since found some better components to use, so now the diodes are 1N4007, the capacitor in the RC filter is 1000uF 25v, the PNP transistor is a 2N5401 (good for 150v Vce, so definitely should be able to cope with any big spikes on the noisy side of the filter), and the resistor on the base of the 2N5401 to switch it on is 8.2Kohm.
Thanks for all your help,
Daz.