Talked to a very good electrician today, who did my bathroom wiring. He said:

• A timer costs around $100
• I'd need a larger relay. While a $100 timer can switch a 13A cylinder they tend to wear out pretty quickly. Another $100
• 1.5 hours of time

Total around $400 inc GST. My best guess is this could save 20c of power per day when prices are low, 50c on an average day, and $1 or a bit more on a day where evening prices are quite high - late summer, early winter, or any time the hydro lakes are low. Given they're turning off another power station in a year or two the payback time could come back, I doubt it will get worse.

So I think the payback time is at least a year, probably two years. Not sure it's worth it for the money, more for the interest factor. If I could get the parts and install cheaper, sure it's worth it, but $400 is a lot more than I expected to pay. I'll get onto my neighbor the electrician to see if he can do it cheaper before I decide.