It is a fuel problem. Coils get hot. You have to disconnect line at carb, put line into a clear bottle, take off center tower wire on dizzy (so it won't start), crank motor, observe steady/pulsing fuel into bottle. Should start to fill up quick. Make sure it's strong squirts. If good, it's the carb. Don't care if carb rebuilt or not, don't care if bowl full.
If does not supply good volume of fuel into bottle, it's pump and on back. See if you can use the choke to keep it running. Best to have a remote start
switch so you can stand near carb for all this.