maybe unbolt the axle sensor, clean it and bolt/glue it back on. Don't glue the bolt threads! your gluing the surface to seal out the moisture and prevent rust, the proper stuff is some kind of epoxy but all i ever used is a thick Loctite gel and some super glue activator to help it set.
Thats a big old leak then! wont be the timing case, has to be the oil cooler, was the whole cooler replaced or just the gasket?
was the engine cooked? common in the MLT 627, also common for head gaskets but not for leaking that kind of oil quantity!
I say its the oil cooler or a cracked block?
See my post above, calibration will be the same on yours.
BUT you almost certainly have a fault.
Common for the sensor on rear axle to fail or the wires get chewed or damaged, if the wires short together it normally knackered the read out box.
Replace the sensor first as most common then fit...
Assuming it's an old 630. Pull the box out, ideally pallet forks and 2 x big fert bags at the ready.
On level ground take the forks off, ift boom fully in the air.
Small hole in back of read out box, poke and hold the reset button in with small allen key or something till it beeps once and...
The big 40amp fuse under the cab does not supply just the transmission, if its blowing or bad connection you need to fix it but otherwise it will not have any effect on the transmission.
if your loosing drive only when the transmission is hot then the transmission clutch packs are simply worn...
Levers are common to fail, but as you lost both directions, check the transmission fuse in the dash.
check you have oil pressure in case the pump has failed, do the main hydraulics work? damper coupling between gearbox and engine fail sometimes.
I think its a 629?
if so then this varta would be my first choice.
that actually looks to be a very good price for it too after a 2 minute...