It looks to be a better insulated tank to mine, I have not until last few months used electric to heat the water, but used oil, in the summer it would switch on three times a week for ½ hour a time, but would normally cut out after 20 minutes, it was only used for hand washing, and boiler is 20 kW, it was not really enough so water only warm.
So around 7 hours a week with a 3 kW immersion would keep water warm for hand washing, my showed is around 10 kW and used for around 20 minutes a time, so a shower will need around another 3.5 hours to heat the water. So two people who both shower every other day one would consider it would need the immersion to run for at least 5 hours a day to get all the hot water required.
I now use electric for domestic hot water in the summer, I can't in the winter as no way to turn central heating hot coil off, I use no timer, it is left switched on 24/7, however there is a sensor on the supply cables so it only heats water when would would otherwise be exporting power from solar panels. It does tell me how much I am using
and how much used, and also says when the thermostat has switched off, it says water hot, so I know when it is working, and I found the thermostat had been set too high and the over temperature trip had turned off the immersion heater, if this happened to your lower immersion heater you may not realise it has tripped.
With my system it can use much less than 3 kW due to the solar iboost+ which controls it, so hard to see from the electric meters if working, not got a smart meter yet, but would assume they do have some thing like this
which shows you what you are using, maybe something like this
so you can see if the immersion is using power. I will admit my standard electric meter is a bit useless, the old wheel type you could see the change in wheel speed, but newer types harder to see what you are using.
I would have thought with all electric you would have a variable tariff, and today to get a variable tariff you need a smart meter, except it seems in Scotland where economy 7 can still be installed. But going by what I use to heat water seems likely simply not left on long enough.