First, the power supply was only dishing up around 9 volts which fell to less than 8 by the time it reached the gatepost. Luckily, its a PSU salvaged from an industrial-strength network switch, and the output is adjustable with a small potentiometer, so a quick twiddle and voila! around 12 volts at the gate.
Still erratic in operation though :-( A bit more research later and I think I've found the cause. The Vellemann kit is designed to run off a couple of 9 volt PP3 batteries, one each for the transmitter and the receiver, and their web site/forum says that its OK to run the whole shebang at 12 volts. However, I discovered that if I drop the power to 9 volts on the receiver and leave it at 12 on the transmitter the instability goes away - no idea why, and finding out is well beyond my electronics knowledge. I've added a simple 9 volt regulator in the box and all seems well.
Just as well, as Mrs Grizzly was getting increasingly ticked off by trekking out to the gate to find the box was empty - a bit ironic, as when I announced I was going to make this gadget I got the standard roll of eyes and 'what on earth for??....' :-)