Immediate thought would be using Latching relays trigger by the turn signal pulse.
If the other turn signal is switched, it removes ground of the previous latching relays then latches the other side giving you the other view and vice versa. Relay to remove ground on hazzard button with diode in the event of 4 ways.
Don't know if taking your eyes off the road to glance down at the monitor is a good idea though
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