There's a few ways to do it without taking ALL the gears out.
Some people just slosh kero or degreaser in there then tip it upside down...
I find the best is take the big speedo drive cover off the LH side, remove the mainshaft bearing retainer, slide out the layshaft then roll the cluster gear up on top of the mainshaft. Easiest if you pull the oil feed pipe & strainer too, then you can remove the cluster..
Then tip the box forward a bit, slosh some degreaser/diesel/kero/etc in there- get your hands and a brush in and clean it out pretty good without pulling the mainshaft apart.
If the layshaft is toast (as is common) replace it and the cluster's needle bearings.
OTOH, if you don't know it's good, strip it completely... you never know what you will find.
I found an S box had been assembled by the PO without the mainshaft nose's needle bearing... after the cluster had lost 4 teeth and 2nd gear, 3 teeth, and we stripped it...
BTW have a squiz down into the diff while you rock the couplings. If the planet (spider) gears rock around on the diff pin, replece them and the pin.
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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.
