If you’re talking about the pin to attach the sear to the action, I usually use a thin Phillips screwdriver or a small Allen wrench that is about half the size of the pin. It makes it easier to line everything up. Then slowly use the pin to push the Allen wrench back thru the hole. You will have to jiggle the parts around as you do it. I am pretty sure My target and standard triggers have the same type of sear spring.

Can you post some pics of the different springs just to clarify.

Not sure why you put it back in the stock to test it if you can’t get the correct pin in place and the safety doesn’t work? That worries me a little bit.
The sear and safety aren’t engaging because, a) you’re using a smaller diameter nail as the pin. And b) the new trigger is probably out of adjustment cause it has never been mated to your action assembly. Or any action if it’s a new trigger and sear from Gunshack.
Once the correct pin is installed the trigger can be properly adjusted and you should be good to go.
Please do not try to use it with a homemade nail pin as the trigger pin.