If you find it works with battery charger connected I would assume it poor connection and voltage drop issue.
Could be just coincidence & it always best assume nothing and test everything so the S wire to the starter solenoid wants be proven be always good when key turned to crank .
A quick way determine ground side issue is use a jump lead from battery to block ground and test starter function, test the battery terminals for voltage drop first though .
You only got 2 + powers to starter, main heavy direct from battery (no relay as the solenoid is the relay) and the solenoid control wire fed from ignition start position .
Use a test light and/or DMM to test for poor connection at various connection points, test battery terminals too, don't forget to test both sides of connection terminals/crimp points etc to try determine exact point of voltage drop or perhaps no solemoid control voltage from ignition when turned to crank .
Don't forget voltage drop needs be done on a loaded circuit, if you don't really understand voltage drop testing youtube will help teach the basics .
A link to a basic starter test principle, same test basics can be used on any electrical connection/circuit with some cognitive thought to find problems .
https://www.youtube.com/watch?v=_xvddRJmkAA
Once you understand the principles the testing becomes easy & you don't throw new parts at it as you can do diagnosis rather than tryagnosis ...
By
Mr B ·