That's the "beauty" of using a small bulb. At low currents, the filament stays cool and has a low resistance. If the current increases enough to produce a little light, the resistance goes up with temperature. When it is sized properly, it acts as a somewhat constant current source, not "constant", but it flattens the curve (and then fuses if the current gets too high!).
I don't know if they list the wattage of the dome light, but if it measures 1.5 ohm with a meter, at 12 V it would be 18 watts if that R didn't increase. I'ts probably less, headlamps are generally ~ 55 watts. At .7 ohms and 12 V (and cars are actually closer to 13.6 with the alternator running), that would be over 200 watts - so you can see the effect. You could also try measuring the dome lamp current at 12 V, I bet you see far less than the 8 Amps you'd expect at 1.5 ohms.
And you won't see any voltage drop across the bulb until you add a load to it, otherwise it just acts like a wire. OK, it looks like you did hook up the lamp with the zapper as a load and saw .2V drop. That makes sense. I'm guessing the zapper isn't that sensitive to a little over-voltage, I doubt those landscape supplies are well regulated, and probably many do run right off of "12 V" batteries. But if that concerns you, I'd use small diodes to drop ~.7 V for each diode. Your 10 ohm R is only going to drop ~ 1 V anyhow. Can you measure the current for the zapper? Might need to sacrifice a bug, the current might climb while it is actively in "execute" mode (or it's just discharging the cap, no effect on source current)?
I'm also curious - do you know how many watts your solar panel for the fence charger is rated for?