If the neutral switch is bad the rewiring won't help a bit. The rewiring is for when the wiring harness & connectors start to cause issues which will eventually ruin the neutral switch, starters & ignition switches.

^^ if the neutral switch is bad what will re-wiring it accomplish?

When you are there and it does not start run a wire from soleniod terminal on starter (small spade terminal on its own) and touch it to the positive battery terminal if the starter cranks over rewire soleniod wire from ignition down to neutral start on top of transmission. If it does not crank correctly check earth terminals on engine.

I agree w/ bbforks, these trucks wind up with a series of partial opens in the wire harness connections that together add up to enough drain to prevent starter operation as it will not be able to provide quite enough current to completely pull in the starter solenoid. {does the starter run if you jumper directly to the wire connection that energises when the key switch is in the start position?}, but then gets intermittent (sometimes hear a click when in neutral, no click in gear, but starter does not turn, maybe hitting the starter, or moving the directional lever seems to fix it some, a jumper on the neutral switch may help for a while, and it has the same feel as just about like a bad/dirty battery post). This is usually worse in trucks that were LPS rated when new as the voltage drop in the LPS disconnect box is one of the worse culprits, but the key switch and neutral safety switches and their connectors are all part of the concern and usually about equal in the cause and effect.
The local Toyota dealer will try and sell a complete wire harness or replace the truck with a newer unit, as the 'correct/warranty-able' repair.

Thank bb, I was thinking asian system. I have had issues with the neutral safety acting up in those trucks also.

I've found Toyotas (especially the 6 series) to have wiring harness issues. I'd take all the main wiring harness connectors apart & check for burning, corrosion, etc. Most of the time, that's where the challenges are.

The model number is 42-6FGCU18. When the lift will not start there is nothing going to the starter. The dash lights up but the starter will not engage. This only happens once in a while not everyday or once a week. The lift is only used about 10 hours a month. Jumping the battery does not help. Any suggestions would be great. Thanks for the help.

To give an informed answer a model # would be most helpful. The model & serial #'s are stamped into the frame on the right side (as seated). Should read something like 02-5FG25-68014.

I would start with draining the tar out of the lp regulator. If you get a lot out it could need to be rebuilt or replaced.