A body tie rod end to center link issue

Sounds to me like you have either switched center link, or are trying to put the thing in from the wrong side. Or, you have an oddball end off something else. Does the direction you are attempting to insert it match the other studs? Otherwise pull the opposite end tie rod end and compare the ends and or test fit

You can switch center links between 67--72 and the 73/ later, BUT there are several pieces that MUST "go together" regardless of the actual year of the car. Idler arm, the pitman arm (and the box, larger/ smaller splines) and the center link must all be either pre 73 or 73/ later as the insertion angle of the tapers is pretty much opposite