All the factory manuals for the T603 are available for download here:
Jordan Sales, in Post Falls Idaho, seems to have the largest stock of spares of any of the dealers, and will drop ship to you if they need to order from TYM. At least they did when I ordered he rear hydraulics kit for my tractor from them.
The TYM part number for things from outside sources, at least on my T233, is the subsystem manufacturers part number with some numbers on the front. I‘m guessing it is similar to the old Sears scheme. Where the manufacture code was the first three characters, and the rest of the part number was the actual manufacturer’s number for the part. Example, the Craftsam Table saws were made by Emerson Electric, whose manufacturer code for Sears was 103. So all the part numbers for the saws started with 103.
If I drop the first three numbers from the TYM part number for things related to the Mitsubishi engine in mine, I can successfully find the Mitsubishi parts online. Typically for less than the TYM Dealers want, if they can get them.