Its probably the parking brake. It was on my '05 JD250. The brake is applied by a spring, and released/ held off by hydraulic pressure. The drive shaft goes from the motor, thru the brake housing to the chain case. My brakes had been rebuilt the spring before i bought it in Sep with only 935 hours. It had a slow leak on the right side; i didnt track the leak to the right chain case for about a year. When the leak became a stream, i finally took it to a dealer who found a bad seal in the park brake.
Like your buddy's, mine had to be filling under pressure, but it was overflowing from the breather cap. I pumped 10 gal from the chain case and used a dipstick to measure the distance to the oil surface. then i started the engine but did not disengage the brake; the fluid level in the chain case barely move in 3 minutes. Then i disengaged the brake (which as i understand it sends hydraulic pressure to the brake assembly. The fluid level in the chain case raised 1.25 inches in 3 minutes. Sure enough the mechanic confirmed a folded seal or o-ring in the brake.
Caution. When the mechanic called and said he needed to check why the seal failed, if i had said, "just replace the seal", it would have been only about $1100 to $1200 or so, 14 hours according to the book plus a seal kit. But i didnt realize what was happening. I thot he meant he was going to look around some and run his fingers along the seal surfaces, check for looseness etc. But, when i said "ok, sounds good", he used that as authorization to disassemble the drive motor as part of his investigation. i just wanted the leak stopped, but before it was over, i had a new drive motor and brake combo because putting the drive motor back together would cost only a hundred less than a rebuilt motor/brake combo ( the motor cant be bot separate from the brake, they come as a unit - go figure). $ 2200 for the rebuilt motor/brake. even tho they honored the 14 hour quote to remove/ replace the brake, the total still came to $3700. Pocket change for the pros, but a cashed-out cd for a DIYr, especially when it should have been a third of that. oh well, just remember when his mouth stops moving, grab you wallet tight and ask him how much that changes the cost.
ps. if the leak is minor, just drops or tiny puddles, it seems there may be little downside to just adding fluid. In my case, it wasnt made worse by adding fluid and going on, and the cost skyrocketed for other reasons, not because i added fluid for a year. Sure, at 30 for five gal, it adds up. But i used mine for 150 hours over a year and a half just adding a little each time i started it. Plus it was down a month even after i got it to the dealer. Dont know if I"m right; youll have to decide. Good luck.