A spring on the linkage disengages the starter on the original starter. Passenger cars and COE trucks of this era used a solenoid attached to the starter that had a spring in it to disengage it. The design you originally had was much more reliable than the solenoids that were attached to to the starter in that era. GMC used the mechanical starter switch on their 6 cylinders on 6 volt through 1955 and on their 12 volt 6 cylinders from 56 through 1959 and they worked fine. A simple switch like red58 linked and cleaning the lug fixed them.

I would have never soldered like you did. If you didn't get enough heat to the lug, you will have a cold joint. If you got enough heat to it, I would have fears that you damaged insulation insulation inside the starter.

I have done a lot of soldering in my life. I started with tube and chassis radios in the 50's. The only wire I solder on our trucks these days is the 4-0 battery cables. I use Kester 44 old stock that I buy on eBay that still has lead in it. Years ago I soldered a lot of wires on trucks. Now I use crimp connectors that have heat shrink on them. I learned many years ago that solder cracks with vibration just like welds. My father in law was an aircraft mechanic during the war and I have had several mechanics during the years in my shop that had a lot of experience with aircraft maintenance.