You disconnected the main power from the battery...(to replace the dome light fuse), then all this started to happen.
If you jumper the main solenoid pick wire you can engage the starter directly.
So going back, you never disconnect the power lead at the battery, you always disconnect the Ground First.
Then the power...
I would be thinking that it is time to start replacing the main cables on your car, and the ignition switch.
If your grounds are still original that is unshielded twisted, they are probably really full of dirt, and corrosion.
You can use two off the shelf cables from a parts store. On the battery end you can get one of the with extra power take offs pig tails wires and do away with those various ring connectors that are attached. Main from battery to frame and frame to engine/tranny.
Same for the main power cables, get the ones with the extra pig tails and splice in to your main cables going back to the fuse panel and the extra ring connectors so there is minimum ways to have things attached to the battery.
Using push buttons to get around things is ok, but later on adds another thing to worry about. Getting it back to the OEM, and such is the good way to go.
But re-reading your original post this all started when you were disconnecting the "Power side" of the battery, and I think you are missing this. There are about 2-4 wires branching off the main power lead, and a flakey connection there can cause a variety of issues with back feeding things through various circuits....Electrons are sneakier than you want to imagine....They use different things to get what they want...or need.
The starter switch is a funny thing... it has a key in detect, off position, a run position and a start position. The Start position backfeeds to the run, but doesn't power the Load reduction relay. This relay cuts power to the head lights a/c circuits, (heater blower...) and a few other things also called the "X" circuit as that is the name of the wiring trace.
Adding a heat soak relay is a must on Automatic Cars, I know as I have 2 of them..the starters being under the Exhaust manifold even with the heat shields in place can get heat bound, or old and not start after a 20-30 minute drive until they cool off. The heat soak relay shortens the run of wire from the battery through a relay to the starter solenoid pick wire... you use the oem pick solenoid pick wire from the ignition switch to power the relay when you turn it to start.
Not having a book is a no-no. The haynes is a good thing to have, it is all I used to keep my 81 running for over 20 years...
Another good place for you to go is Chris's electrical wiring pages, down load them and get to know them...
http://chris.chemidl.in/vw-wiring-diagram-pdf-1982-1983-1984/
Sure your 81 isn't listed, but the only book I could find for my Rabbit was a 78-80 Haynes...but I know it is really really close....so are Chris's pages.
The ignition switch takes a lot of abuse, and lets see if yours is still original that is 2019-1981= 38 years old... it too is probably tired...
On the early VW's it is easy to replace and takes about 20 minutes. Order 2...
http://www.mk1autohaus.com/Ignition-Starter-Switch--Meyle-_p_6808.html
mk1 is a good place to get parts from, I have been for about 20 years or so, and Moogie, (AKA BEN) is a good guy and he doesn't sell crap parts.
I think that if you get back to the basics, you will find that you will fix your issues....