Hi,
I can think of three immediate possibilities:
1. The battery isn't as good as you think it is. Sometimes a battery will read good voltage and appear to take a charge, but just isn't up to a heavy load like the starter. The best way to check it is to attach a voltmeter to the battery and then put it under load, watching for a rapid voltage drop. (To some extent, another test is if the car starts with another car's battery jumpered to it.)
2. The starter solenoid might be going bad. When they fail, there are often symptoms just like you describe. It could also be problem in the starter itself, such as worn out brushes or a shorted out winding, but just based on personal experience, I'd think the solenoid is a bit more likely to fail first. Is the solenoid separately replaceable on TR6? Are there external connections on the TR6 solenoid, where voltage can be checked, to isolate if it's the solenoid or the starter at fault?
3. There might be bad grounds and/or hot connections at the starter/solenoid, relay and/or at the battery. Enough corrosion on those connections can give the exact same symptoms. This is probably the easiest thing to fix, since all that's needed is to disconnect things one at a time, clean up a little, then reconnect. Some dielectric grease (often sold for spark plug wires in auto parts stores or for light bulbs in hardware stores) can help delay new corrosion on the various connections. At the battery, I'd use something heavier than the dielectric grease - like Vaseline - and/or those felt "battery terminal protectors" that some auto parts stores sell.
I suggest not using steel wool to clean up any of the connections. It invariably sheds some small particles, that rust very quickly and quickly promote new corrosion.
There are times when jumpering a battery to start a car will overcome a partially bad solenoid or compensate for moderately corroded connections. So, don't necessarily assume "the battery is bad" if the car starts with a jump. Only use that for general diagnosis and starting point.
Another thing to check, I believe your car also has a separate starter relay that remotely powers the solenoid so that full power is never going through the ignition switch. If that relay fails, I'd expect no response at all, not "clicking" like you hear. But, who knows, I'm not all that familiar with TR6 wiring, so maybe the relay should be checked, too. Just use a voltmeter and see if 12 to 13 volts is showing at the starter solenoid when the key is turned to the start position. If it is, the relay is doing it's job. If not, then the relay is the problem.
If by any chance the battery proves to be bad, that always leads me to wonder why. Some just start to lose their charge due to old age. Other times, the generator or alternator and/or voltage regulator are the problem, failed to charge the battery properly or even damaged it. Most auto parts stores can test the output of generators and alternators.
Hope this helps.
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