[Alan A]

Had a 73 and a 71. Have a modded 250. Had a few other Rumfs too.
I’ll paste the 6-pack buyers guide for you as a starting point since it’ll save me typing.
Rust is the biggest thing to watch for.

Triumph TR6: Pre-buy Inspection checklist

Bodywork
Take a strong flashlight & shine it up in the corners of all 4 fenders...the backs of the rear & the fronts of the fronts (up by the headlights). Check for corrosion.
Take a good look at the backs of the b-posts (where the doors close in the wheel wells). Check for corrosion.
Get in the boot (trunk) & unscrew the cardboard panel so you can see the tank. Check condition of tank and surrounding area.
Pull all the remaining trunk panels and pull the spare tire & look at the trunk floor. Check for corrosion.
Take your flashlight & shine it up along where the convertible top would attach on the sides...snaps down. Another common rust spot.
Either pull out the battery or get down on your knees & shine the flashlight up inside the cockpit where the battery would be. Check for corrosion
Check the rear valence outside at the bottom & get under the car & point your light toward the rear. Check for corrosion.
Take your fingers & run them along the inner fenders where the outer fenders attach. They sometimes rot there & you'll never see (find out) it unless you run your fingers in that area.
If the owner will let you - try pouring a couple of cups of water into the fresh air vent. About one cup should drain out behind each of the front tires. Nothing happens, then there's a rust problem in the wind...and a soaked cockpit. One side drains, then the other side is acting as a reservoir and a potential rust pit...if notalready in that condition - and very well hidden and difficult to correct.
Frame
Take a screwdriver & start poking at the trailing arm sections. Look for signs of "bulging" at both ends of the trailing arms. Do NOT be shy about poking pretty hard. If it's solid, you won't hurt it. Most of the time, the frame will be fine until you get to the trailing arm sections, solely due to the total oil loss system, inherant in every Triumph!
Look for any obvious bends in any of the front sections. Chances are good that there are cracks...that you won't catch unless all the undercoating is removed...again inherant in most cars.
Observe door gaps...top & bottom. Indication of possible frame sag which is difficult to tell when just eyeballing a car.
Check T-Shirt (Cruciform) pressings in front of the differential, look for any bulges or obvious corrosion.
Check rockers (sills) and outriggers both sides, common area for corrosion, expensive to repair!
Electrical
Check all external lights for correct operation, including licence plate light.
Check all interior lights for correct operation, including gauges, courtesy and glove box lights.
Check all warning lights and buzzers.
Check horn.
Check cigar lighter outlet (if fitted).
Check radio (if fitted)
Under bonnet
Check battery terminals and cables for corrosion/oxidization.
Check HT lead, coil, condenser, plug wires & caps, distributor cap (for cracks) and points for wear/pitting.
Check fuse box - correct fuses, signs of burning, no nails! (should be 20 amp if American replacements or 35 amp, ONLY if they are Lucas originals!)
General condition of remaining wiring etc. including starter motor and alternator.
Engine
Do a compression/leakdown test.
Test condition of thrust washers by pushing in on crank pulley as hard as you can. Once in, have someone depress the clutch and using your fingers as a guide, see how far the crankshaft moves out. Acceptible limits are .007" to .013", or the thickness of a fingernail. Alternatively, use vernier calipers if you have them.
Before starting the car, when cold, have someone start the engine and look for blue smoke from the tailpipes.
Check car will idle with choke on and, when warm, with it off.
Get the car up to operating temp & verify oil pressure.
Check engine area for obvious oil, coolant or head gasket leaks. Include oil and water pumps/thermostat housing. Look under car on floor for stains etc.
Check fluid levels, coolant, engine oil, brake and clutch master cylinders.
Running Gear
Jack the car up at the rear (using a block of wood under the jack face) & firmly hold each rear wheel top/bottom & try to wiggle the wheel...do the same on the sides of the wheel. Check for any play. You're testing to make sure the hubs are OK so you don't kill yourself on the way home!
Repeat for front wheels, additionally checking steering arms & track rod ends for play.
Check all bushings...see if they are neoprene & that ALL the bushings have been done, if seller says they've been done. If original, check condition.
Check steering rack, arms and boots for wear or splitting.
Check for play and any excessive movement in steering column, up, down and side-to-side.
Check condition of brakes, discs, pads, drums (rear), hand brake operation etc.
Transmission
Check smooth operation of clutch and listen for any "whiring" sound when released, could be sign of a worn throw out bearing or broken pin.
With clutch depressed, check gear selection for stiffness or sloppiness.
Thrust washers......easy way to make sure is to push the clutch in while at idle & make sure the RPM's don't drop.
Check the clutch linkage down by the gearbox, make sure there aren't any "extensions" on it. Should beconnected by middle hole of the three available.
Check travel of clutch before it engages. If it engages at the very top of the travel, it's probably worn out or, at best, needs serious adjustment.
Check prop shaft, universal joints etc. for excessive play. On some models they have grease nipples, others the UJ's are factory sealed and can dry/wear out.
Test Drive
Check general handling, brakes (pull up in a straight line), clutch operation, gears etc.
Listen for any clunking sounds from the rear-end, could indicate broken diff pin mounts, worn U joints or differential gears. Could also indicate corroded frame which is flexing.


PM me if you need an opinion on the one you are looking at.