I get the feeling you want us to let you alone and you want to go see the guy in town who likes old stuff. I don't think you realize where you are. You are in a forum with hundreds of guys who know 1000 times more, and "like old stuff" more, than "the guy in town". It seemed you ask for help and were frustrated with ordering wrong parts. We fully understand that. This is why we are helping to get you the exact right part. We need a little time and info. We responded in 60 minutes and three on the same day. It seems you had the answer before the weekend was over. Not bad. If you want us to go away, we will. But I need to explain things to you for the sake of members who have tried to help and the worldwide reputation of Stovebolt. As a member, you should welcome that.
I don't know why you ordered the one from Chevs of the 40's. It is obviously wrong. I posted part numbers and stated they should be confirmed first because I looked up 1958 CAR, like you said, and that is the one given. We can only go by the info you give us. It is the same info you will give to the "guy in town". Only he will see the unit, we have not seen any pictures. Oilrag has dissected a little farther and did the confirmation. He used the starter serial number and gave you the drive unit according to that number. If you would give us the casting numbers/stamped numbers on the motor we can be sure even more. We won't go by what you say, we will go by the numbers. We do try to act like we trust the person, just to be polite, but we don't.
The following is not an explanation of what exactly is wrong, just food for thought, some logic for your consideration. I realize you didn't ask what is wrong, you asked for a part number. When someone already thinks they know what is wrong, we tread lightly on their opinion.
As you know, the foot start mechanism has linkage and about five pivots. It is possible that these joints/pivots are worn. It is also possible that the drive clutch is weak. If the pinion gear or the flywheel gears are not badly worn, and you report no engagement and no grinding, seems to eliminate gear tooth problems. The pinion gear is supposed to engage all the way or bump against the flywheel BEFORE the button is pushed. So if it is doing that, that is normal. You say it spins about 25% of the time without engaging. That is due to lack of spring pressure (the spring you see on the drive between clutch and "pulley"/sheave) or lack of pressure from the foot mechanism. A bad drive clutch wound slip after engagement. The symptom you describe is "spins without engagement, sometimes". That's all we know. The 75% engage and 25% not engage seems to point away from clutch or bad teeth or something broken. EXCEPT the spring mentioned or foot mechanism pivots/linkages are loose, worn or broken.(wallowed out). It could be that the button pushing lever is good and the pinion sliding levers have lost their leverage. Due to wear, not enough pressure left when your foot bottoms out.
KUDOS to Oilrag-Tom, Jerry and Glenn
You will get other info and opinions. If you want them.