Toyota Repair: 1996 toyota tacoma starter problem, starter solenoid, jumper wire

Question
This is a 1996 toyota tacoma. A/T and approx. 115,000 miles. When trying to start there is just one click from starter solenoid but starter does not engage. The starter was replaced and still the same problem. The battery was tested and is good. I can feel the relay clicking when trying to start. I even pulled relay and jumped terminals 3,5 and starter solenoid clicked. After New starter was installed the truck did start once. This leads me to believe this is a wiring issue, ignition switch or park/neutral switch. Battery terminals are tight and ground to frame is too.how should I proceed with troubleshooting this problem without replacing a bunch of components. If you think it is the ignition switch do you replace just the tumbler or the whole switch. Thanks for your help.

Answer
hello, with the truck out of gear and the key out of the ignition use a long jumper wire from the positive terminal of the battery, disconnect the small solenoid wire on the starter, connect one end of the wire to the solenoid then touch the other end to the positive battery cable, does the starter turn the engine over like this?