Looking for a picture of a 1969 624 international tractor motor.picture of the motor broke down.

Check with parts Tree Reair Clinic

Check the fluid level, if ok be sure the selector spool that linkage is attached to is not broke and has full up and down movement with no obstruction on the down side. If spool is moving properly the clutch pack may be burned up.

Incorrect valve adjustment, especially on OHV motors that causes a backfire can cause the sheer pin to break. Obviously this saves the motor from worse damage. Also, sudden stops caused by hitting something like a log or stump with engaged blades have broken the pins before. On an older motor I had one sheer because the piston rod was a little loose off the crank and the slop was causing the motor to bind. Obviously this did internal damage but the sheer momentum of the motor spinning a heavy flywheel no suddenly stopping broke the pin. Lastly, the magnets on the flywheel could be hitting the coil pack, binding up causing the pin to snap. Be sure to check if the space is gapped correctly. And don't buy cheap pins or generic pins. There should be no slop whatsoever. You almost have to pound it into the slot. Slop equals a much high ER chance of breaking for no reason at all.

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It is called dieseling. Could be carbon on the plugs or in the combustion chamber. Carbon gets hot enough to cause fuel to keep igniting after ignition is turned off.

drive belt broke if transaxle is not turning does clutch pedal feel loose ?

it sounds like a major engine problem either it dropped a valve or broke a connecting rod out a small long screw driver down the spark plug hole and turn it by hand with the screw driver down the hole and feel if the connecting rod is moving

Looking down on the engine from the flywheel side the engine rotates c/w.

looking down at the terminals, rotate push-button to the right. the wiring sequence is R, W at the top, then Black (in, from power source) , Black (out, to motor).

THIS SOUNDS LIKE A THROTTLE CABLE LINKAGE PROBLEM.WITH THE HOOD OPEN AND MOTOR RUNNING RUN YOUR THOTTLE UP AND DOWN WHILE LOOKING @ THE LEFT SIDE OF THE MOTOR TO SEE IF THE CABLE IS FROZEN IN PLACE OR BROKE OR DISCONNECTED .HOPE THIS HELPS

go to sears.com and you can get the manual and the parts you need.