A standard 5 pin relay will do the trick. Connections are as follows
Terminal 86 12volts from ignition switch originally connected to your solenoid
Terminal 85 ground
Terminal 30 12 volts from battery , from battery stud/connection to this terminal
Terminal 87 12 volts to solenoid
Relay should have a built in mounting bracket. Mount somewhere close to the starter to reduce the amount of wiring involved and for a neater install. front brace is found on V8 applications supporting the front of the starter motor. There could be other reasons for your problems however install relay it will only cost a few dollars cheap and easy install which will deliver a good battery voltage to your solenoid bypassing the ignition system.