Garage Cabinets, Garage Storage, and Garage Organization

Hi.   I'm after some advise on the "T" bar selector of my 65 Mustang auto tranny.   It takes maybe 30 secs to go into gear when put into reverse and sometimes doesn't go into drive at all unless I slide it back and forth and then maybe wait a while before it decides to go into gear.  This mainly happens when it's cold, usually ok when hot, but not always.  I know and appreciate that it's not young & probably the original which is not contacting somewhere because of wear, but what do I actually have to replace to fix it.  It's starting to happen now most of the time.  Any help much appreciated.