I don't know what you mean about TA22 radiators being on the wrong side: All Ta22 had the 2T/2TG which had a passenger side water inlet, and also the passenger side top hose from radiator.
If your seeing one with the drivers side outlet then I suggest it was an Ra model (hence the 18'R' motor which is on the other side) or someone has just put another radiator in it. I just you get yours re-corred if you want. And the top hose outlet should be on the passenger side, if it aint... you ain't got the original radiator.