Ford F-150 - 1997-2003 :: 2001 V8 Not Starting - Only Click Once When Turn The Key

2001 F150 4.6 V8 Triton

Automatic
Battery Tests Good
Starter Tests Good - I saw it spin and come out at the testing station at Autozone
Ignition Relay (the one in the fusebox)- New (8mo.)
Switch on the firewall on passenger side of truck - New (8mo.)
Battery terminals/connectors - Tight, no movement, Cleaned within the last week.
Starter connections - cleaned within the last week.

I am having trouble with my truck not starting. The issue has been occurring on and off for over a year. Usually, it happens about once a month, regardless of weather.

I turn the key, and there is one click. Usually at this point, I can use one hand to gently pull the shifter "up" towards park and turn the key again and it will start. Recently it is not starting when I do this. I have tried many times, and have tried to start it in Neutral (is that even possible with an Automatic?).

With the key in the "ON" position, I go under the truck and jump the starter cellinoid. I am jumping the small post to the big post where th wire comes from the battery. I do not touch the post that the wire goes into the starter.

I am very confused because it starts just fine without fail and almost instantly when I jump the posts. It is drive-able this way, but I would like to resolve this issue, and resume using my key to start it since the issue doesn't seem to be resolving itself as it usually does.

A friend told me about the Ignition Starter Switch inside the Column. If I have time I will attempt to start the truck with a screw driver on the switch tonight to narrow down the issue.