Ask a simple question and what do you get? Lots of answers of varying degree of complexity
No need to use logic chips, these are prone to failure in automotive applications anyway.
Here's what you do: ( sorry, it'll have to be a word picture as I do not know how to do the other kind)
You need two relays which have SPDT ( changeover) contacts. You use only the N/C (closed when UN- energised) contacts.
Brake to one relay (1) N/C contact, blinker to the other relay (2) N/c contact. Other contact end of both relays are commoned and go to your lamp.
Now the logic : relay 1 gets powered by blinker, relay 2 by the brake.
So, whats happening is, each time a signal, brake OR blinker, arrives the other input gets turned off by the relay - bulb lights on either signal.
If BOTH signal arrive then BOTH relays turn off - bulb unlit.
As the blinker is an intermittant signal you might just get a very brief flash from the lamp, depending if the relay turns on faster than the filament lights up or not in the case of both signals being present.
Klaus