Hi,
There has been a ton of discussions here on BCF about using the Delco 7127-3. With some minor modifcations and tweaking, that will work in your car and is very widely available and cheap (usually $45-$60 rebuilt). Just search the BCF archives. This alternator will put out around 60-65 amps, compared to the 22 amps your TR's generator will produce at best.
The only downside of the 6127-3 is that it's not any lighter or smaller than the original Lucas generator. (I'd love to find a smaller/lighter alternator that produces 45 to 60 amps, if anyone has a suggestion.)
There are also several very detailed discussions on the web regarding how to install it: try VTR.org's maintenance section for one. Google for others. ISTR most recently Tinster put one in his TR and posted some photos about it. He did disassemble the alternator in order to paint it, which would only be for personal preferences. (I'd suggest not disassembling it, probably voids any warranty.) Another tip, there will need to be some grinding done on the alternator case to make it fit (see the various articles, you'll see why) and care needs to be taken to not get any of the grinding grit into the alternator, so tape it up to keep any waiyward dust out of the armature and bearings.
Also, you'll need to decide if you want to convert to a thin belt or keep the wide original. If wide, you'll need a special pulley for the alternator (most come with a thin belt pulley). If changing to a thin belt, you'll need compatible pulleys at the crank and at the water pump.
Thin belt conversions can be purchased as a kit.
This change is often done when converting to an electric fan (which ideally needs the extra output of an alternator) and removing the 4-blade fan and it's hub/extension from the TR engine. If this is done, a harmonic balancer/pulley is needed at the crankshaft. (Some just run without the fan extension or balancer, but that's not recommended for the engine/gearbox, long term.)
There are a few photos of the 7127-3, thin belt conversion, harmonic balancer and electric fan installation on my TR4 (identical with respect to these parts on your car), at the link below in my signature.
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