At the end of August, I ordered a pack of cassettes and a cable for the tape player.  The cables and tapes came in the first week of September, looking good.

I pulled out my tape player and set up my TI.  When I got ready to hook up the tape player, I found the tape player I had does not have the correct speaker jack.

Rather than trying to find an adapter that may work, I will go online and find a TI Tape player designed for the TI 99/4A.