I installed a J-type in my MKII GT6, it took a bit of fabrication and minor cutting of the propshaft tunnel, and new rear gearbox mounts since the J-type is longer.
Paul Tegler helped me install it, it's documented on his web site. The safron/yellow GT6 in the photos is my car.
https://www.teglerizer.com/triumphstuff/gt6/gt6jtype.htm
Not a project for the uninitiated, but it would have been easier if we had all the parts ready: we had to custom-fab the gearbox mounts out of angle iron, and then fabricate all the wiring. I got the gearbox from Quantumechanics, BTW.
If I had it to do over again I'd install the correct D-type overdrive. It's less expensive, mainly, and requires no cutting (although the J-type required very little cutting, actually). However, the J-type is a bit more robust. But for normal driving the D type is fine.
It's the most useful mod I did to this car, transfored her into a top-end screamer! Just loved that OD.
Let us know what you do . . . and good luck! :thumbsup: