I agree with Harry on the axle tests. And will add that it is common for a axle needing repair to leak a
lot of oil ouit by the one or both wheels. So look at the inner surface of the front wheel and tires. My guess is it is the front axle, but just how bad is it? They can be anwhere from easy to unrepairable...although I have often wondered if a clever mechanic could put one back together as a 2wd axle.
At the worst, maybe you could find a junkyard 1725 2wd front axle and still have a decent tractor, That would buy time. If you can find one...... Otherwise an axle can be a long project. You must be a pretty good mechanic to be willing to do a front axle, so not much I can help you with there.
I like those old Fords. Nice engine, nice loader - be sure to get the FEL bucket with it. If I were bidding on it, it would be with the idea that it might end up being a 2wd. Nothing wrong with that if the tractor is priced low enough.
Maybe I can add a few more things to think about tomorrow.
First thought is that with 20% tread and a nice Woods loader that tractror has probably seen a lot of 4wd use. We know that hard full time 4wd use leads to front axle repairs and sometimes to front driveshaft repairs, but rarely do we hear about transmission repairs. Especially on old style sliding gear manual shifters.
As for transfer cases, I am not at all sure that 1725 tractor even has a transfer case. What makes you think it does?
I looked at the exploded diagram on Messicks.com and don't see a typical automotive transfer case. Maybe I missed it. Look for yourself. Here's a link. BTW, Messicks has all the 1725 parts books online.
Now take what I say with a grain of sat, because I have NOT worked on that particular Ford. But have on earlier ones, and most manual shift japanese tractors from that era are pretty similar to each other. I just do not recall one that has a complex transfer case. Why do you think it does....or is it more about not wanting to split the tractor?
Instead of a transfer case with offset shafts and reduction gears, compact tractors tend to have a simple splined sleeve-joint collar that slides on a shifter shaft when you move the 4wd lever. The 4wd lever moves the splined collar back and forth to engage the front drive shaft to the forward end of the transmission main shaft. It's pretty simple design. Hardly ever gives a problem.
At the auction, you should check the 4wd engagement lever. Put the tractor in gear, rock it back and forth while trying to move the 4wd lever. You are looking to see if the 4wd lever seems to be connected to something internally. If so that's good. In fact, even if the lever won't move that internal collar, that is still OK - because it probably just means the internal 4wd collar's shifting splines are not lined up.
What you don't want is a 4wd lever that is totally loose & feels so disconnected that it's not doing anything at all. And even so, fixing a 4wd shifter problem is no more work than a front axle repair, and probably cheaper.
Luck,
rScotty