You can sort of figure out the series resistor value of an LED. A small one like an idiot light draws about 10 milliamps (you can measure it), the LED has ~ 3 Volts across it so you need to drop 9 Volts.
9 / 0.01 = 900 Ohms, that would be the minimum in reality it could be much higher like 1-10 K Ohms, you really need to read the specs to figure it out.
Back to the topic
When you put the "controle light" in the socket, does it light at all? If not its shorting the socket out and all four flashers are getting power, this happened to me also, as a temporary fix I snipped one side