Brake booster/master cylinder "throw" required

[XXL]

How much throw is required on the rod/shaft thingie to properly engage your run-of-the-mill GM booster and master cylinder?

That is... how far does the shaft that stabs into the booster move when depressing the brakes?

In my new cab, I'll be locating the booster and master cylinder under the passenger side of the dash (don't ask... I was dropped on my head as a baby ). I'm going to have to make a bellcrank mechanism to turn the brake pedal moving axis sideways and drive a rod side to side under the dash to press the booster/mc. What I'm wanting to work out at this point are the dimensions and angles for the linkage.

Here's a reallllly bad sketch of what I'm contemplating...