The 350 and all engines are a dynamic work unit. The rotate and every engine cycle they push out 350 cubic inches of air. It runs and runs and runs that way because of all the engine parameters that make it run.
THERE IS NO WAY AN ENGINE CAN BE IN A "FALSE NEUTRAL" IF THE ENGINE IS STILL RUNNING!
I suspect it may be the lock up clutch in the torgue converter. I want you to locate the brake light switch. It is under the dash at the upper swing angle of your brake pedal.
Locate the purple wire coming from the switch and cut it. It doesn't make any difference which side. There is one purple wire going to the switch and one purple wire leaving the switch. Make sure you tape the ends and leave enough room for it to be attached again.
When you apply brakes the torque converter unlocks, that is the reason the signal is routed through the switch. It will not affect brake lights.
The purple wire provides the 12 volt signal from the computer to lock up the torque converter when you reach a certain speed. With out the signal the clutch will remain static and the transmission will operate without the 250 RPM drop after the torque converter locks up..
If the torque converter clutch is defective you will certainly get the "false neutral" effect. When it trys to lock up is slips and doesn't lock up immediatly.
If the false neutral doesn't occur, then have the torque converter replaced. It sometimes is not part of a rebuild and somethimes they put in an after market rebuilt torque converter that is bad. Make sure you reconnect the purple wire.
In my 40+ years of garage ownership I have seen this problem a number of times and it is most always the torque converter.
If it is the torque converter don't wait too long to have it fixed as it can cause transmission damage if driven at high speeds and on a long trip. Around town is OK.
If you don't get it repaired what will happen is the converter will lock up and won't unlock and you wont be able to put it in gear without the engine stalling and it will be time for the "hook truck".
Let me know and good luick
Monday, May 29th, 2006 AT 8:33 AM