Brakes "skip" as I press down. Whats goin on?

Oh okay yes. I understand that. I did some more searching online and the most similar issue I see that compares to mine is "hard brake pedal" and Im seeing "lack of vacuum pressure ." as a common cause.
OK, first We need to be clear, from the pic You posted You have a single reservoir non-power assisted master cylinder for a four-wheel drum system. No vacuum involved
at all, and no differential or proportioning valves either. If a wheel cylinder or hose or steel line fails anywhere in the system, You will have -0- pressure & -0- pedal, NADA!
This is why the above posts recommend a switch to a dual reservoir, but without the differential valve added to the system as well, You're not much better off.
The only way that car is going to "grab & release" is because the drum surfaces are screwed, it's manual unassisted brakes, regardless of the hydraulic conditions the
pressure ain't going to change itself no how no way. Certainly not in a rhythmic way. Either You've got a good pedal or You don't, it's that simple. If it's leaking/losing
fluid, don't operate that car at all, get it fixed before driving it....period!