Hooray! Managed to get the Tamron TAP-in console working, updated the firmware on a lens from version 2 to version 4, and found that a previous owner had changed focus settings for different distances and zoom range steps... which could explain some strange previous results when using the lens. Might have been okay for their camera. Changed everything back to the default, for now, but this/or another photo notes a previous owner's settings, in case they were better, which I doubt.

The TAP-in console's a gadget that connects to some Tamron lenses and permits updating firmware, as mentioned above, and altering some settings in the camera to improve the likes of autofocus accuracy, and image stabilisation operation. A potential hazard of buying second-hand lenses that can have had such things adjusted, is that the previous owner(s) may have changed something by mistake, or to suit they're specific camera and usage. To the unsuspecting later buyers, that could make the lens appear to be a flawed or faulty.

As usual, bought a faulty one for peanuts to try and fix. There was no USB cable supplied, and I suspect the company selling it made the same mistake that I initially made, and tried using a cable that was lying about, only to find the thing didn't work. The reason it didn't work in my case, was that the cable I used was just intended for charging another device's battery. Only the power connection wires were connected, the data wires weren't fitted/present in the cable, so the computer couldn't communicate with console. A bit of hunting around the collection of all sorts of USB leads came up with a much posher looking one, and that worked... which was something of a relief, after previously taking the console near completely apart a few weeks previously. It had been particularly fiddly putting it back together.

Sigma have a similar device for their lenses, but a newer approach from some manufacturers, is to fit a USB port/connection on to their lenses.