So, on that tailpiece the axle or pivot shaft is also a torsion bar type spring, the spring is pinned to the body on 1 side, pinned to the “floating” part and free to float in the other socket of the body.
Your only problem is if those pins are a “no drift” type pin (in other words you can only see one side of the pin – where the pin is punched into a hole that doesn’t go right through).
Turn it over and if you can see both side of the pins you’re doing fine – go to your local hardware store and spend a few dollars on a pin punch, or as we call them in Canada a pin drift, of the correct size.
Drop some oil over the pin locations some time before you’re ready to work – support the piece around the pin location as you punch it, but leave a hole in the support piece for the pin to fall into – and punch the pins out – flip the piece and re-assemble.
That’s my take on it anyway…