Murray with BS not running

I have a Murray Select 13.5 HP riding mower Model No. 405000X8F with B&S 21B807-0296-E1 date 2/10/2005. It cut off after about 5 minutes of mowing and would not restart. The motor would turn over real fast. It had no spark. Changed spark plug and put on an armature/magneto/coil from another mower and it ran good. Purchased a new coil and replaced it. Then it would spin but not run. No spark again. Replaced new coil with the old one that had been working and it would still not run. Now it will run if I remove the small wire from the bottom of the coil. I checked the ignition switch and it checked good with a meter according to the wiring diagram. I cut the wire from the M terminal at the rear of the ignition switch and it would run with the wire still attached to the coil. I then ran a new wire from the ignition switch to the coil to check to see if the wire between the ignition switch and the coil was bad and it would not run. I am assuming all the safety switches are working properly since it will engage the starter,but I am not sure if that is a correct assumption. Could it be a bad ignition switch, even though it checked good with a meter, or could it be something else. Any ideas on what to check next? The fuel shut off solenoid seems to be working correctly and will shut the engine off in about 2 seconds after turning off the ignition switch.

If the darned thing runs with the "kill" wire from the ignition system disconnected, YES, the ignition switch or associated wiring (or possibly some safety component) is bad.

The mag ("armature" in Briggs parlance) is self-contained and makes spark on it's own without any connection to, or power from the ignition switch.

I would replace the ignition switch. Get the OEM switch, or the correct aftermarket switch, not a 'look-alike' from the box store, it may not work. (And it will drive the next guy nuts trying to figure out the problem.)

Change the switch. Does this machine get stored outside? Water in switch and there are tiny litte springs that rust and break. They push on little shoes that slide back and forth. When you get and replace 5he CORRECT switch, and your mower is now happy and running, take that old swich apart. You will find lots of rusty or corroded crap in there.

I had a dirt dobber plug the ign. sw. on one of mine. Went to ebay and using the pinout from my wiring harness (looked at the pins on the switch) with the shape/color and the pictures that are displayed on top of it identifying the switch positons, I searched for similar looking items. Found just that, great price, fast shipping, and the rest is history.

Update, Installed the correct B&S ignition switch and still having the same problem. Any more ideas as to what to check?

to be sure, check the clearance of the coil to flywheel. Should be around .010 ". I've seen this scenario before and good to check or recheck this.