+1 for all Dan's suggestions. The last being the fuse block. I cleaned and soldered mine. Also there is a relay on the right side wall of the engine bay (forward one) that operates the turn sigs.

I haven't had an electrical or turn signal issue since doing this upgrade for six years and my mini is my only car and sits outside.

If you have this type of fuse box, it won't fall apart if you remove it. Just take out the 2 mounting screws and carefully turn it over. If you remove any wires, label then first. Disconnect the battery before touching it - some fuses are live even with the key off. 

The back is open to the elements. The brass clip at each end of a fuse is riveted to the brass terminals for the wires. Corrosion breaks the conductivity and causes intermittent problems. 

If anything falls apart, you'd be way past needing a fuse box.

The 12 volts at the flasher comes and goes. Now it's gone. So is 12 v on at the flasher with ignition on? Then when you move the stalk it sends voltage thru the flasher to either side of the car? That's why there are 2 wires on that side of the flasher? Before I pull the fuse box and have it fall apart thought I'd ask some questions. Thanks!

Fuses can be fine but the connections behind them may be crap!

Pulled them and used a meter to determine if they were good because a visual inspection sometimes doesn't show a bad fuse. 4 ways are out too but I guess that's to be expected?

When you "metered" the fuses, did you measure the resistance across the fuse itself, or from input wire terminal to output? You should track voltage along the circuit from source (battery) to destination (light bulb), checking each connection along the way. You can do it with a volt meter though a test light of similar wattage to the turn lamp will tell you if the voltage is good under load. A no-load test might show a solid 12V but with a load applied to the circuit, you'd see a voltage drop after a problem connection.

See also this thread:

https://www.minimania.com/msgThread/128894/1/1/Electrical_gremlins

Routing the speedo cable I pulled a wire off the flasher. Put it back on and signals worked but flasher was getting hot. Replaced it and all good until they stopped again. Metered fuses all good, have a new Lucus stalk which I plugged in so original is still good. Even tried another new flasher and still no signals. All of the other lighting and brake lights work?