I have an '84 repair manual w/ wiring diagrams in it.
There might be something 'vert' related in there. I'll have a peek tonight.
The 'main-relay' 83GT was refering to, is the #1 relay. It's found behind the air-cleaner chamber, and is bolted to the shock-pillar. That's not the same part you're dealing with here.
I don't suspect either 'main-relay' is your problem.
It's likely the rear-seat switches paul-p referred to, or...
I've seen this in action on a working 1985 system.
The way it is supposed to work is this:
"With the e-Brake ON," you press and hold the button on the center console.
The system releases and folds the rear seats down, automatically, and then the top goes down, automatically.
My point is: Make sure the eBrake is pulled-up when you try to let the top down.
You might be chasing wild geese, that you'll never catch.
If everything else is checking out good, it's probably all good.
After trying with the eBrake on, if it still doesn't work, look into those seat-switches (over-ride them). But first, check the power top motor, directly to the battery. Perhaps that motor is fried?