There is a "cheap & dirty" way to do this, given two conditions. If your running lights are on all the time, and you have an electronic flasher ( requires no load to flash ) you can do it with a small SPDT relay.
All you do is connect the lamp to the common of the relay, connect the running light wire to the normally closed contact, and connect one side of the coil to the signal light wire. The other side of the coil goes to ground. What will happen is the running lights are powered, and when you turn on the signal light, the relay operates, turning out the light.
If you want to go one step further, you could put 2 suitable diodes in series with the normally closed connection, and connect the normally open to the lamp. This will dim the lamp for running lights, and give full bright for signal.