As noted in other posts....check for rust. Getting a look underneath would be very useful. Also getting a magnet on the sills to check for filler would be good. The sills and the back of the windsheild pillars are typical rust spots, as is the driver side footwell and bottom of the battery box.
Also, check whether this has been resprayed. Hard to tell from the pictures, but it looks like the paint under the bonnet is a little lighter than the outside - one would expect the opposite.
If this car has been in California for some time I would expect the mileage to be higher. Californians get to drive their cars more than most. 52K seems low.
I don't see a commission number or VIN on this ebay listing, which would tell you whether its a California car originally or not. I suspect it is not, because I don't see a catalytic convertor warning light on the dash. I think the Califormia cars had three warning lights on the centre dash, the one in the middle being the cat-light.
Get a photo of the commission plate, which should also give you the trim codes to check paint originality. Late-79 (November onwards) Triumph moved from commission numbers to VIN numbers, but there should be some form of commission plate somewhere.
Also get a serial number off the motor. Says its been rebuilt, but a check would help confirm whether its been replaced.
There's a hundred things to check for mechanically. If you are really serious, try to get an onsite inspection done. I wouldn't buy anything without a test drive.