It's possible that the lead wire is broken, in which case you can purchase a TS-70B replacement part (part # 640270) and solder it to the existing cable.

Often people mistakenly plug the TA-29 into the T1 or T2 output BNC connectors on the front of the temperature controller.  The TA-29 needs to be connected to one of the BNC T2 Inputs labeled "Channel 2" and "Channel 1" on the instrument rear panel.