Anyone know what will dissolve that goo in the back of the factory electronic control boxes?

I would try some lacquer thinner covering the goo and let it sit from 5 to 20 minutes and see if it will fallout or scrape out easier
I remember faintly someone doing that years ago but I can't remember the details now

the next question is, what does one re-fill the back of the box with ?

Non conducting epoxy?

I’m thinking silicone it’s still pliable after 50 years

Industry uses "Electronics Potting Compound"

Epoxy usually.

Easily found on Amazon or many other places

Yeah just mount it on the inner fender of your brand new paint job and it will start melting in a few weeks

I had an orange box do that before.

Gus

Let me leave it on my shelf for a few years. Mess on shelf then.

I'd be concerned about the temperature affecting the other components

That video was with a circuit board.

For circuit board electronics they are baked on the board in a heated chamber filled with an inert gas which acts like a flux to keep the oxygen out of the solder joints. They are heated a lot more than the 210 degrees boiling water will reach.

Our older stuff was not IC chips but full size resisters and transistors so I would tend to agree with you that they are more heat prone but I think 210 degrees is still below what they see in our old cars in the summer heat.