Open up the dizzy (remove the cap) Look at the plate on which the points, condenser etc are screwed. On this plate, a loadomatic dizzy will have a couple of springs, in very apparent view. The dual (vacuum and mechanical) advance dizzies have their return springs in the vac advance unit itself. The mechanical advance (centrifugal) mechanism has springs as well, but they are under the plate.
second method: remove the cap. twist on the rotor. If the shaft is solid with no play (or perhaps a little due to wear), then you have a vac only dizzy. If the rotor/shaft can be turned about 15 degrees in one direction, and then springs back when you let go, you have a dual advance dizzy.
Don't get confused when people talk about "dual vacuum" hookups. All dual vacuum hookup dizzies have a centrifugal advance as well. The second (outer) vac hookup is a retard, for polution control stuff.
As you are probably aware, your carb looks to have a spark control valve which is supposed to be used with a loadomatic dizzy. Carb looks to be a Motorcraft 1940, which is not original, but it was Ford OEM replacement for many years.
If you have a loadomatic and conver to the Holley 5200, you will need a new dizzy too. And that mean a new Pertronix unit, as the old one will have a "D" shaft, versus the new one will have a "C" shaft.
later.....