I went to the John Deer site, and I'm assuming you mean the plunger head pitman, or what I would call the connecting rod, from the crankshaft, to the plunger head. John Deere shows it not to be available, but to call John Deere, and see if there is a substitiute part.
There is a serial number break in the 32xxx area, that the pitman rod was a different part number. You can go to J.D. main site, enter the baler model number, and it will bring up an exploded view of the parts, by section.
What I came up with is part #AM 3106E, but they want you to search for the part number without spaces, so AM3106E.
Being it will be a while until hay time, you may want to try a search on ebay, I'd suggest using "John Deere 14T", or the above part number. Save the searches, and anytime the model, or part number come up, it will notify you. Parts for the 14T seem to show up there pretty regular. In fact there are a few on there now from a guy parting one out. In his listing, it says to contact him if anyone needs any other parts. It says parts come from a working baler used last in 2007.
I bought a pair of NOS bill hooks for my 14T several years ago, for around $30.00. New ones at the time were $35+ each, so that was a deal for me.
Another option is to post a free "want to buy" a on TractorHouse. That option is in the top left corner in the red. I believe 3rd item down. You will need to register with them, and enter some contact info. I have had good luck using this to find parts for my older equipment. I have gotten replies as quick as 3-4 hours after posting, up to 5 days later. All depends on the season I guess.
Here is a link to TractorHouse:
http://www.tractorhouse.com/Defaultind partsaspx
I went ahead, and did a search for salvaged 14T's on TractorHouse, and came up with these. Just remember it takes one from in the neighborhood of serial # 32xxx, and above. You will need to go to J.D to get the exact number break, and double check the number I found.
Here is a listing of salvaged 14T's
Farm Parts, Tractor Parts at TractorHouse.com
I believe I'd call J.D., and see if there is a replacement part available, from like a 24T. I know some parts will interchange, but not sure what all. But do expect to receive some sticker shock... But, that is a starting point on price. Then place a want to buy ad on TractorHouse. I'd say you'll get more than several responses. Most definitely ask by part number.
Most of the balers where I did the model search above don't have the serial numbers listed. However, there is one in the 48xxx range, so if the pitman is decent shape, it should fit.
Again, please double check all the numbers I posted, as it was somewhat of a quickie search....
Hope this helps..!!