Of course, that's not an issue. Just how much more is what I'm wondering.
I've seen anecdotal evidence that keeping your gas boiler on 24/7 in the summer costs 25% more than using it on a timer. I suspect with an electric element the % difference will be lower, but,of course, the difference in cost per kWh may be more relevant than any efficiency differences.
Edit: Regardless, I recommended a time schedule in post #2 because it will clearly save them some money. I just don't want them to think their water heating bill will reduce by 75% by only having the water on 6/24.
OK, you asked for it, but we'll have to delve into basic thermodynamics to set the scene, and even then there are too many variables to calculate properly.
A tank of hot water will lose heat at a rate determined by its insulation properties and the difference between the water temperature and the outside air. So it will cool from 60 to 59deg slightly faster than from 59 to 58. When it reaches the air temperature, it will stop cooling at all.
So, in reverse, to heat it back from 59deg to 60 will use more power (ie take longer) than from 58 to 59, because it's losing heat faster. The difference is tiny, but it's there. The effect is that it takes a little bit more power to maintain the water at 60deg than to let it cool to 50 then heat it back to 60. In a well-insulated tank, it might take a few hours to cool to 50, but only a few minutes to heat it back to 60. Compare that with maintaining it a 60 throughout. Without knowing all the relevant factors, especially the efficiency of the insulation, the thermal mass of the towels in the airing cupboard and whether you open the door to take the vacuum cleaner out, we can't estimate how much would be saved, but even though it's small, it's not zero.
The more the water cools overnight, the greater the savings. If it actually gets to near the air temperature, so that it stops cooling significantly, then the savings can be much larger. Suppose it stays cool like that for two hours. Then it's not losing any more heat, but if you'd kept it hot you'd have wasted two hours'-worth of heating power.
As you point out, gas and electrical power are different. With electrical heating - no power wastage and instant on/off - it's always better to switch it off overnight, using experience to judge the timing. Any saving, no matter how small, must be worth having.
With gas, it depends on the efficiency of the insulation. With the 60->50deg scenario, it might be worth leaving it on, though I wouldn't personally. If it cools more than that, it should be switched off overnight. You should always switch off space heating overnight.
Hope this is what you wanted.