international L 162 questions

You could post a photo of the ignition switch.

It may be original or it could have been replaced years ago with an off-the-shelf generic ignition switch.

If it is the latter, then I would buy another off-the-shelf unit and next I would try the new key. !!! It may fit and work.

If not, replace the switch. Label the wires when you remove each one.

EDIT: I am also a professional, a licensed professional ! Thank you, thank you very much !

If the switch is the original with a press button start, the positions will be. Key out, straight up and down. One click to the left or counter clock wise is accessory. One click to the right, or clockwise is run. A replacement switch may have a second clockwise to the right for the key activated start function. You do not have to use this.
I posted a Cole Hersee link. Check it out. Now you have all of the information you need from a professional. I have more than a dozen OEM ignition switches, all from IHC L&R models. All of the keyed switches are COLE-HERSEE. Only one or two sets came with the keys.

I went to your link but it has a ton of them i bought one that i thought would work put it is a normal off-acc-start. Do you know the model of the one that will fit and be correct like the original?

Welcome aboard and good luck with your L.

Try a Pollak 31-122P switch. 3 position - Off, run, accessory.