I expect you have spikes on the 12V (and thus 5V) due to switching the light on/off coming from the relay contact. (NOT the coil as you have flyback diode).The 555 is sensative to spikes (having tried that in the past). I do not see the schematic, but try to work with a small capacitor on the 5V line near the 555. The fact that is works better with a normal multimeter connected could be because it acts as a capacitor to short circuit the spikes. Google on this and you will find many articles.
Paul