I suppose if you have transmission leak, washing off the housing would be an OK method. It's a lot more realistic to remove the fill plug (17mm allen socket) and see if oil runs out with the car level to the ground. If oil is coming out, you might just have an engine oil leak. You should be able to smell the difference, as gear oil has a sulfur smell.
If the gear oil is low, put your finger in the oil fill hole and find the oil level. If it's down 1/2", it's about 1/2 a quart low and you have a leak. The transmission only holds 2 quarts. If it's low, it's most likely a seal. Fix it.
On average, I'd say any transmission over 200,000 or 10 years usually has a transmission axle seal that is leaking and should have the gear oil changed out. I would bet a leaking seal is the #1 reason for destroyed differentials, particularly if it's an 01M, as there is only about 5/8th of a quart in the differential case. Not enough mechanics realize it's a separate reservoir for the differential.
There are actually several different axle flange bolts, depending on the year and model. An inexpensive XZN triple-square driver kit with a 1/2" hex drive can be bought in a box set at most of the retail parts stores for around $10-$12. The set will include sizes between 6mm - 12mm. Or there is FleaBay...
https://www.ebay.com/sch/i.html?_nkw=xzn+bits
It's a simple rule for axle seals: If it's leaking, replace it.
When refilling manual transmissions, don't buy into the gear oils that say "GL-4/ GL-5". It can't be both and the sychronizer rings need the GL-4 gear oil. GL-5 tears up brass synchros.
