Brake pedal assembly to push rod?

I upgraded to a dual master in my 65 mustang. I'm at a bit of a loss as to how the new much longer push rod attaches to the pedal arm.
Originally there was a piece that went between the two, it's in the picture below but I don't even recall how that worked.
Is it possible that with the new setup I remove the arm with the switch on it and connect the push rod in place of it?
 

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That looks nothing like the push rod that came out of my '66(Mine was just a standard rod that connected directly to the pedal instead of the...bar that you have there. That being said, looking at the picture it looks like your intermediate piece there attaches through the hole at the end of the bar just as you have it sitting there and the push rod would then attach to the cotter pin clevis?

My push rod looks like this:

vN5DPuq_FhQBJ69khv_rHk52_Tk4RW8-1wLL_wy_pKWHc4_LgU.jpg


I have manual brakes and an I6 setup though...but most of pictures I google show the same as above. What kind of brakes did your car come with?
 
I can't find anything that looks like my setup, totally strange. It's a factory 289 power brake car, upgraded to front discs.
I removed that mystery arm and it looks like the push rod from the new dual master will hook up to the pedal arm like yours did.
This car has more weirdness than you could ever imagine. I can't even remember half the odd things. Lowering springs raised it about 2", what's the deal with that!