Cranks fine runs 5 mins shuts off?

CODE P1300
We've replaced the igniter. The igniter gets really hot idling 5 mins or drive for five mins.
1994 lexus es300 cranks fine runs 5 mins then shuts off. Will not fire back up for 10 to 15 mis. Not over heating, replace cam and crack shaft sensor and Ignition ignitor my mech has lost his mind with this car. Just checked with the Mech and he said the Ignition Ignitor is getting really hot. The old one and a used one we got from salvage yard. Gets hot when the key is turned on and the car is not running. When something cools down say 20 to 30 mins of sitting car cranks up and idles with no problem or will drive with no problem for 2 to 5 mins. The computer tester only gives the code for ignition ignitor. No other codes or problems are returned.

Already Tried:
Cam & crank sensor Ignition Ignitor fuel pump & filters Started off running 15 20 miles then down to 5 now 1 maybe 2 miles. Simply stops running like running out of gas. Pressure is good on fuel. Used to let it sit on side of road 5 mins then drive another 5 to 10 mins. Now it has to sit for 15 or 20 mins to even start back up and can't drive more than 1 or 2 miles.
Diagnostic code after ecm cleared and the car runs for 5 mins then shuts off is P1300 The ignition ignitor is getting rather HOT to the touch after it runs for 2 to 5 mins then the car simply shuts off and will turn over but will not attempt to fire for the next 20 or 30 mins. I sprayed duster upside down on the ignitor last night to see if that would cool it and make it run but it did not help

code is for a shorted out coil which if it's shorted out will cause the ignitor to overheat have you changed any coil packs

MY MECH IS PULLING OUT HIS HAIR! I know you all make make a lot of money but mines really tight right now and the mech is a friend of mine so he's helping me out alot but I think he's at a loss for this one.

I am having the same problem with my 94 lexus es300. You said you changed the relay and it stopped. What relay are you referring too?

The Relay I'm talking about is on the passenger side on the right. There is one screw you have to remove you can turn that screw by hand. Once that cover is off you'll see a black relay and a fuse in there.

What was the solution to this? I have a 95 lexus es300 doing the exact same thing! Need fixed fast please help was gonna get new ecm but idk if I should waste the money if thats not the problem. Same exact issues and codes!

It has igniter code but I have replaced with new already. Code still repeats to come back. I will take off battery and let code clear and will run for anywhere from 30 min to 1 hour then stall again and not start.