Yep - that top diagram is fine - with a fuse at the battery.
The strobed brake lights get tricky because of the multiplexed module output. It's be easy if they were common GND else +12V.
But using a relay or transistor to strobe them may be ok.
A relay is ok if the flash rate is not too fast.
Otherwise a transistor or MOSFET which is simpler if the brake lights are GND switched - the switcher (transistor, MOSFET or relay) then merely connected in parallel with the brake switch.
The relay or transistor or MOSFET is energised/driven by whichever of a+ or b+ you want to use, noting a+ & b+ won't be be the same as a particular strobed LED - it might be +12V all the time or whenever a- or b- are "active".
But a- or b- could also be used.
But first need to know whether the brakes are +12V or GND switched, and which module output is the pulsed output - is it (a & b)+ or (a & b)-?
The latter is simply tested by connecting one 12V LED from a+ (or b+) to GND, or the LED from +12V to a- or b-.
That determines whether a more common NPN transistor or N-channel MOSFET is used for the input for the strobed brakes else the less common PNP tranny or P-channel MOSFET.
Similarly for which type is required for the output (power) to the brakes - NPN & N-ch if ground switching, or PNP or P-ch if +12V switched.
If using a relay, the polarity of the input signal (a/b+ or a/b-) is not important (merely ground else +12V connect the other end of its coil), though you must know whether the brakes are GND or +12V switched. Either way it is the same relay (ie, SPST relays are not N-type or P-type), though a transient-protection diode must be used across the relay's coil to protect the module outputs from coil-induced voltage spikes. (Hence by tradition fixing the +ve (86) and -ve (85) ends of the relay coil - the Kathode or line-end of the diode is connected to the +12V end.)
Others hereon are better for opinions on relay speed switching. I do not consider them suitable for fast strobing (eg, police & emergency vehicle strobes), however after recently seeing relays used to switch lights to music, I know they can work - but I don't know how long for (still the normal ~1 million operations?)
Another consideration is incandescent versus LED brake lights.
Each incandescent brake bulb is probably almost 2A (21W) compared to maybe up to 100mA (1.2W) if LEDs. That can impact relay contact life and transistor/MOSFET sizing.
Furthermore, incandescents have
thermal inertia and take longer to light up and extinguish than LEDs, plus the thermal fatigue from switching ages the bulbs.
Hence a flashing incandescent might only last hours or days, plus they won't have the crispness of a strobed LED.
And if the strobe pulse is to short, the bulbs may not light fully.
Though those can be overcome (trickle-current resistors to pre-heat bulbs, and RC delays to extend on time), it'd be better to get the LED brake lights.
And don't forget that if you change left-right indicators/flashers to LEDS, you probably need change your flasher can/module. (Some electronic types can be modified - just change the value of its
current feedback resistor.)
But don't get those expensive resistor ballasts to solve that issue - that undoes the "power saving" of the LEDs. (IE - those resistors are the equivalent of the original ~21W incandescent loads that were replaced. In fact I usually recommend using cheaper incandescents instead....)
As to a 3pst switch... WOT? And undo all that switch work?
But you might be right, and they do exist. But I would still prefer your 2 switches (cool man!) and relays - hence whether you have 3A or 30A or 300A loads it doesn't matter - ie, the common 30A relay is fine for now. Increase its rating later if you have to, but you'd use the same buttons.
How about a 3p4p switch to go back to a space-saving single switch? Nah - I still prefer 2 switches for earlier reasons (simpler wiring, independent) and no (off-)on-off-on of (say) the rears to get to both (off, rear, front, both).
But in whatever case - relays. That means a greater selection of switches since they probably only need to be rated for 0.5A - 1A.
The only mod I'd envisage over 2 buttons/switches is a 3rd if you want ONE to do both, as well as the
existing 2 individuals.
Does that sound appropriate to you? IE - low-power switches to control relays of (say) 30A?
Normally the relays would be outside the cabin to be more inline with the light power wiring, but I presume in this case the strobe module is inside (the cabin), and the (or 2) relays are probably to be on/with the module (unless the on-off clicking noise is problem). But it should still reduce the heavy power wiring to the switches if the module is under-dash (but still suitably accessible for pattern adjustment) - not that 0.5A to 5A wires makes that much difference (I'd probably use 5A wire for both). But later if extending to 30A etc.
Not that I have checked your power/current calculations...
I also hope the strobe module remembers the last pattern chosen between uses...