This comes up every so often...I assume the deal is that the starter whirs, but refuses to engage the flywheel?
The gear in the bullet nose is entirely inertial. So it depends on the weight of the gear, the freedom of the gear to slide along the screw shaft, and the torque of the starter to spin up fast enough to move the gear down the shaft. It's such a simple assembly that there are only a few things to go wrong. Areas to look at:
1) Is the starter getting full power from the battery. A weak battery or bad connection can slow the starter spin-up, which doesn't provide the inertia to move the gear to the flywheel. Dirty contacts in the solenoid could also cause a slow spool up, as will a partially shorted field or armateur coil in side the starter. If you hear the starter winding up to full speed within one second, then this is not your problem. If it takes 2-3 seconds to wind to full speed, then the above could be your problem.
2) Corrosion or hardened grease inside the bullet nose. If the car ever sat for a long time, the gear can get sticky on the screw shaft. It could be light corrosion, road dirt if it ran without a clutch cover, or just old hardened grease. I think the starter bendix assembly gets well lubricated from oil slinging off the flywheel from the back of the scroll seal, so as long as your TR gets run often, the bendix stays lubricated. But, grit and dirt can accumulate...light corrosion can cause binding. If the starter winds up within a second, then this is your likely cause. The solution is, of course, to pull the starter and fully clean and lightly lube the bendix assembly. Make sure there is absolutely no sticking or binding in the gear. You can try cleaning without disassembling the starter, using carb cleaner...or take the nose off to do a really good job. I'd just try it assembled first, though.
3) It is possible you have a mechanical problem in the starter. This would include a broken spring, so the gear does not return to the home position, the rubber shock drive deteriorating and sending rubber into the assembly, or a "C" clip out of position or binding. Unless it was assembled wrong, I doubt this is your issue, though. These are pretty robust starters. The rubber shock drive is the only part that wears...and if that were bad the starter would never engage. Once the rubber drive fails the gear cannot ever be driven.
4) If you hear the starter hit the flywheel and then it spins freely, there is a chance your have the wrong flywheel for the starter. If the starter used to work fine, this is a long shot.
That's all I can think of. If I were diagnosing, I would check the electrics first, followed by pulling the starter for a cleaning. 99% chance those 2 actions will get it going again.