Actually, most recent vintage japanese and american cars and trucks have flasher circuits that are designed to blink faster when there is a bulb out. This is often the only way you'll know you have a bulb out, as most people never walk around their cars. As you might imagine, a fast flashing turn signal will nearly always get you a "courtesy stop" if a cop sees you, which can result in a bonus for them if you happen to have any problems outstanding.
The old thermal flashers were of two types, one a simple two-prong device about as tall as it's diameter with a thermal disc that was heated by the current flowing through it. It would "pop" over and break the circuit after a bit of time, then cool and reset the circuit. This type would stop blinking, or blink really slowly when a bulb was out. using one of these and connecting a trailer (additional bulb(s)) would result in a really fast blinking... The second type was usually two to three times diameter and often with three terminals actually contained a timer of sorts and relay, and was often sold for "trailering" where there were more bulb. These typically had a relatively constant rate that didn't depend on the load, as long as at least one bulb was working. This type was bad because you couldn't tell if a bulb ws out, but was good because you didn't need to swap the flasher when you hooked up the trailer...
--Rick