Yes - glad you're feeling yourself again
5 gallons a day - strewth ! ! My first thought was to combine the idea of leaving a tap on with the need to supply water to Neddy - which leads me to a short (promise) story
I built the central heating controller in 2001 (now that is a long story ! ) and the header tank does not have a ballcock controlling the supply - it has a 12v solenoid which is switched via some simple electronics which senses the level in the tank from a couple of reed type level sensors in the tank. (Upper sensor switches 'water top-up' and the lower one means 'insufficient supply' and shuts the system down.)
The valve in the feed line has been adjusted so that when the solenoid is operated the flow is 1 litre per minute. There are a couple of cheepie alarm clocks on the system - one by the header tank and one in the control box in the kitchen - the batteries of these are disconnected until the water feed solenoid is powered so they only run when water is being fed to the header tank. The clock dials have been replaced with ones that say 'litres' because 1 minute = 1 litre and so both clocks display the total number of litres supplied.
This could be useful in checking the health of the system but in practice the clocks never get looked at - they were useful in setting up the system though - knowing that it contains 76 litres told me how much anti-corrosion jollop to put in.
There's a 'but' here though - the flow of just 1 litre per minute doesn't keep the pipes clean and in particular allows any muck that gets to the solenoid to lodge there and reduce the flow which screws up the calibration of course.
But you could build a timer device that operates a solenoid on full flow intermittantly - set to provide 5 gallons a day - or put a reed level sensor in Neddy's drinking trough and top up the trough several times a day via a Smiths clock timer - that should help to keep the supply clear of ice.
I would guess that you're thermocouple cable is er.. low cost
![Smile :-)](./images/smilies/icon_smile.gif)
but if you have any corrosion problems with it then stainless steel wire could be used but you'd need to insulate it - good source for wire is
http://www.wires.co.uk