I don't know about the ST2040, so this is just all made up. But I think it is very similar to the Mitsubishi 2050,
according to Buck at EFC. If the information I have is correct, that means it should have a 4 cylinder Mitsubishi K4C engine (Should be stamped somewhere) and might be similar to the Bull series of tractors. It may also be similar to the next size up, the Satoh 650, 670, and ST2500 series, which have
two separate reservoirs, one for hydraulic fluid and the other for gear oil.
Check over CAREFULLY for any dipstick. Sometimes they are hidden in nearly impossible to see or find places.
I think there is a fill level bolt hole in the side of some of the Satoh/Mitsubishi tractors. With the machine level, you pull that bolt out, and fill the reservoir until it just drips, replace the bolt, and the tractor is full. The ones I have seen are on the left side of the transmission housing, roughly where one's ankle would be. I don't know if that is accurate for yours.
When you find all this information out, please take photos and post them here with any other information you find; it helps expand the body of knowledge.