The MASTER is like the IGNITION SWITCH.... When the vehicle is powered power, "ignition on" or "auxiliary on", power is available to the "module".
OK, then diode "wire or" a constant drive to the lamp that's off. What that means is the drive to the transistor or the mosfet can be "wire ored" with 2 diodes. One for the mosfet/Q1 and one for the constant on signal. Or just OR, both signals and drive the mosfets. Might be easier. You don't need two power mosfets per bulb.
You can't tie both lights together and make the WigWag work. They have to be isolated to make WigWag work, unless you have switching. The switching can be two transistors or a mechanical three poll switch.
Diodes and more wiring you are talking about is simpler than two transistors? Could you sketch that out.
I appreciate your ideas but to explain how the circuit works, I am sure you know, for the record, 2N2222 is "inverting" the signal for the M2 MOSFET. The 555 sends out a positive square wave. This drives M1 OFF, drives Q1 ON, pulls M2 low, drives it ON (and lamp on). The 555 then goes low, reverses the process, drives M1 on, and Q1 and M2 are off. This goes back and forth with the square wave, 50% duty at about 1.5 Hz, each on or off 0.333 seconds, alternating. M3 and M4 just bypasses the WigWag... with solid state switching.
I could forget both M3 & M4 and go with a toggle switch, 3-Polls, double-throw with, On-Off-On. This would be a switch with at least a 15 amp rating. When in steady, it basically bypasses the WIG-WAG module all together. For steady it is just straight through the switch. A switch like this cost about $10-$14. They are wide, ugly and would not fit in with row of single and double poll switches. That is no big deal. I might go that way, to save the current going through the M3 and M$, FQP27P06's. I will get some MOSFET's and see how hot they get at 4.5 amps, no heatsink. I will likely have to have them on the some small heat-sink or greased to the aluminum case it will be in. If they run hot, too much inefficiency, I will skip the M3/M4 and go mechanical switching as plan B.
I like the sound of your idea and think it could be done.... draw it up! With that said I am looking at some RC "astable multivibrators", where both transistors are PNP type or P channel, no inverter needed. See link below. In this case, I might be able to do as you are thinking. Draw it up!
http://www.techlib.com/electronics/flipflopflash.htm
A lot of these RC transistor / SCR flip flops have some things to recommend them, but there are always trade offs. Most of these RC or SCR flip flop circuits have more discrete parts, capacitors, resistors, diodes, four transistors or darlingtons. Some of these flip flops are affected by supply voltage and/or load, changing rate of flash. A 555 timer is precision, not affected by system voltage or load, and they only cost $0.30 to $1.00 each. I also have the option of putting a POT in, to fine tune the flash rate. What the heck! MOSFET's are about $1.00 each. There is no big parts saving or cost savings by leaving off the two MOSFETS. In the trade I get to use a single switch of lower rating. So in "big parts" we are looking at $5.00, top.
There are 100's circuits to do this job and pick from. I admit I'm not sure of what is best. At this point what I have (BIG BIG thanks to RonV) will work. I have to pick one. I'm going to buy parts, prototype it, see what is what. I might try some of the RC circuits from the above link may be. Why not. If I find frustration in cherry picking parts to get flash rate or complicated switching to save two transistors, I will have my answer. I am not sure I can implement simple base or gate switching to do double duty (steady/flash) with the RC circuits. It might take a multi-poll, multi-throw switch. As it is now, I only need a double-poll double-throw switch of modest current rating. Just to match other switches I will use a bigger one verses a mini toggle, although I could with the transistor switching.
If you have a solid idea, could you draw it out, I'd appreciate it. If it's better, less parts, less cost and more efficient cool! I like the idea of doing the same with less parts. The 555 is cheating, but gosh darn it what a great IC. I have made PWM dimmers with them, awesome. They are cheap and flexible. There are no doubt many good ideas... love to hear your idea, but this design can't use your idea directly, with-out being as complex or even more so.