FWIW, my '93 +8 has an LT77 box (actually, an LT77S - the last iteration of the LT77 box), and I believe yours is likely to be the same as mine. However, it is a Morgan.....
Dave
You get the prize, vbalddave!
YES, you have the last variant of the 2wd LT77,
somewhat different than the more common 4wd in that the latter has a filter on a second drain. In other words their internals are the same, but the casing and draining, filtering, filling systems can vary, even within the same vehicle model as the LT77s kept changing as well. The correct choice of fluid is VITAL. LT77s have an internal pump which cannot deal with the regular manual gear oils. They quickly eat their own innards if not properly fed.
(Don't ask how I know and quickly learned the importance of oil viscosity..as in 5 miles). 
That is why LR/Rover insisted on Dextron-3 a now discontinued (Ford) product. Dextron 3 was made for automatic transmissions, a red fluid that is much thinner than traditional gear oils, and something this internal pump can handle. Then Castrol TQF (from memory),
rough shifting, then Castrol SMX-S
(great!), also discontinued, and then Castrol Aircol PD 32, and then a fully synthetic Syntrans Multivehicle 75-90, most of which are not available outside the UK/EC assuming they are still available. In North America I used to use the oil specifically recommended for this box by Amsoil. But I changed my LT77s (3 +8s) to 3 2wd R380s over twenty years ago and stopped closely tracking LT77s and their recommended fluids. I am loathe to suggest anything for a sensitive box if I haven't tried it. But there are still 1000s of LT77s about on all continents.
There is no need for an elegant gear oil dispensing pump, though I can think of many other uses for it. It would actual better serve, carefully used, as a filler. Gearbox-wise such thing are they are used for single access systems.
Did LR decided to block the drain by 1993? 
That would be sad indeed and a recipe for very Morgan and TVR dirty carpets. The LT77 casing casting came with many easy options for them to put in drainage or filling ports. I found my LT77s easy..as I do the more muscly and smoother R380s. And the 2wd LT77 is uncomplicated compared to its 4wd cousins shown above. Please note, that aside from their identical gear ratios, a 2wd LT77 and a 2wd R380, have nothing in common.
The videos are dealing with variants other than the one Morgan uses. VERY DIFFERENT. They look like earlier 4wd units from Defenders or other LR V8s. .
One first loosens the filler access (YOU DO NOT WANT TO DRAIN THE GEARBOX ONLY TO FIND YOU CANNOT OPEN THE FILLER!) then drains the box (no need to flush it) and re-fill it. Have a couple of liters on hand as it takes (again from memory) 1.6 liters, as your Handbook indicates IIRC.
gmg
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