Curiouser and curiouser. HEI's are normally self contained; they don't require an outside controller. The exception could be one that has been gutted internally and had some kind of reluctor and pickup like the pertronix units installed, That doesn't make sense because the HEI comes with a reluctor and pickup to begin with.
By default, if you lift the distributor cap, the first thing you will see is the rotor and under that will be advance mechanism which is a pair of weights that sit on pins and which are held closed by spings. As the engine accelerates, centrifugal force acts on the weights to cause them to spread or open up which adjusts the advance on the timing. When the engine returns to idle, they close up again. If you look below the advance plate, what you should see next is a toothed reluctor wheel that is attached to the distributor drive shaft. What you won't see is points and a condensor, in their place is an ignition module.
The HEI portion of it all is that the coil, which in older units was a separate device, is now mounted on top of the cap. It is removable for periodic replacement of the cap. After that the harness consists of a power lead to the cap from the ignition switch and a three wire plug in from the distributor body/ignition module to the cap. There is another terminal on the cap but that is for the tach lead and unless you have the gauge package, it will be empty.
So I have to wonder, is that controller actually attached to anything and/or doing anything,or is it some kind of leftover orphan from a previous exercise in timing control that got left behind as being too much of a nuisance to try and remove?
Nick