Where is the neutral safety switch located?

Where is the neutral safety switch located? I have disassembled the auto shifter floor console and do not see anything that looks like the replacement part. Is it under the hood? If so, where? Thanks.

Some background: This problem is intermittent, like once a week for last few weeks. When I turn key to crank engine, dash lights come on, horn and lights work, fuel pump energizes, but no crank, no "click". Battery is good and strong, dash lights do not dim when trying to start. New starter put in but only worked one day, then same thing. This makes me think the only thing left it could be is the neutral safety switch. Thanks.