Hy Mike,
In your above circuit you have assumed that the turn signals (presumably V1= turn left and V2 = turn right) switch between 14V and 0V. But, in my experience, the turn signals switch between 14V and open circuit. If this is the case the circuit will not work.
In my experience, the "flasher" is a formA switch, followed by a center-off formC switch (the lever arm on the steering column). The turn lamps have a low resistance to frame ground, so the simplistic dashed box with the two ideal voltage sources in post#2 is an adequate model of what is in a car...
If you insist on me actually showing that I can simulate the upstream stuff in the typical car, here it is:
LTSpice has a voltage-controlled switch, so we define time-dependent control voltages Vflash, Vright, Vleft that are >0V when we want their respective switches to be closed. I show both the "flasher", as well as the self-cancelling, center-off steering column switch (which is really two switches). I replaced the full-wave bridge shown in post #2 with the two-pin bi-lateral LED I mention in post #8. What is important is the direction of current through the current-limiting resistor, R3.
I could also develop a model for the thermal flasher, if you insist... Here I took a short-cut, making the flasher time-based, instead of load current-based.
The important thing about modeling in LTSpice is to come up with the simplest model that reflects reality, without worrying about the insignificant stuff. For example, most cars have another switch between the battery and the flasher (ignition switch) which I didn't bother to model...