Oil In Coolant Speed Triple

Almost certainly head gasket. A pressure leak down test will confirm.

 

Yes head gasket, when you have it apart, again, make sure that the head and barrels are flat, true and not warped

 

Probably head gasket given you've just rebuilt it.
But could be a core plug if stored with just water as coolant in freezing temperatures.

 

AS others have said it does point to the head gasket, however when dismantling the engine often the liners are disturbed, these are sealed at the factory and it only takes a very minor disturbance to the liners and a water leak will occur, it will need stripping back down, checking the head for warping as well, use a good steel rule across the block to check the face, but more importantly tolerances between the liners. Unfortunately a number of speed triples had both gearbox and clutch issues, why on earth Triumph designed the clutch so complex is beyond me, the gearchange return spring behind the clutch is a weak point and was modified for a stronger one (I do have a couple of the genuine Triumph German made ones if you need one). The gearchange mechanism on the shaft has a habit of detaching and falling into the crankcase, it can lead to gearbox failure. One main issue is Triumph use external manufacturers for parts, sometimes they switch to a different supplier mid way through production (supply issues), therefore there is a risk in quality control, it's been like this for years with both car and bike manufacturers. The remedy for the gearchange mechanism is to tack weld it to the shaft, this is a permanent failsafe way to stop this happening.

 

You can use a quality brand silicone sealer such as pro seal RTV, if you go to the bikers toolbox website you will see it, these people are first class and only sell quality products, I have had a number of items over the years and not had an issue.