Relay, On and Off with Turn Signals

This is my first post here ... I have lurked for a while but I would contribute and be part of the group now. I have lots of time in building emergency vehicles but I have a relay question that is kicking my butt. I am working on a set of signals for a motorcycle and have to momentary switches to work with. The idea is when the left switch is pressed the left signal lights and if pressed again or the right pressed it stops. The same for the right side press the button it lights, press again it stops. I have been working the relays many ways but I still get stuck with a third button either +ve or -ve. Any ideas? I really don't want the third button. I love the puzzle of figuring it out, but I am at a loss now. Any thoughts?

I did it with 8 relays, and a flasher for each side. Look at this diagram from the Relay Section: My idea uses two of these, one for each side. The third relay from the left (Relay 3) changes state when the "activate" button is released. Depending on the state of relay 3, the next action of the button is determined. Terminal 87a is ACTIVATE, and Terminal 87 is DEactivate. Both (-) triggers. Run a connection from one side's relay 3 #87 to the other side's relay 3 #87a, and vica-versa. Insert a diode in each wire with the band towards #87a. Push one side for activate, and it will deactivate the other, if ON. If it is not on, some relays click, but nothing happens. The second push of the same button deactivates its side. It will work as desired, but that's a lot of relays to stash in a motorcycle. Perhaps this will give you new direction to come up with something more compact. Have fun, and ride safe.

Thanks for the reply davep ... it is exactly what I want but yes 8 relays is a lot. I am using micro relays but they are still about a half inch wide. I am going to look at this diagram and see is I can break it down. Here is hoping :)

The more I look at the diagram it seems like it could be easier but still working on it. The diagram can be tricky.