SO what I did was trace the route for power to the solenoid. The last 'switch' is the clutch pedal prior to going to the Starter Solenoid. my mod for this was:
I installed a relay after the clutch switch, then I ran a 12v line direct from the battery Distribution block, through a fusible link to the relay(87), out of the relay(30) to the Solenoid.
Off the clutch switch the wire went to the relay(86) coil then from the relay (85) to Ground
I replaced the solenoid contacts as well, as they were pretty beat up and full of carbon
another thing I did was the VATS Bypass (this was done first) but did not fix the issue you are seeing