Hi Sproket, YES.................. it will fit almost straight in. In fact any Triumph 'B' range gearbox from 1950 will accept the 5 speed cluster. Even the Trident cluster will fit, all you need to change from a Trident is the main shaft.
Depending on what year T120, there are some clearances to be made. From 1972 on, these are already there. Before '72, the high gear needs the bore that it PASSES through in the cases, needs opening out, for clearance of the sleeve gear.
The other end of the mainshaft, frist and second are a combined gear. Again the bore that the gear PASSES through needs to be enlarged so that the first / second gear passes through it and fits up to the bearing.
You will need ALL the componants from the 5 speed, including cam plate, index plungers and plunger housing, selector forks and selector rod.
If you are fitting it to a R/H change from L/H then the stub shaft presses right out of the plunger housing and the R/H one presses straight back in. Use gaskets on both the inner and outer gearbox covers.
If your speedo is currently driven from the layshaft, you will have to have it spark eroded to accept the drive gear, if driven from the rear wheel, just go for it. You will not believe the difference it makes

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Roy.